SELINA Solutions for Class 10 Maths Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables)

Mathematics is one of the crucial and most scoring subjects in ICSE Class 10. TopperLearning presents study materials for ICSE Class 10 Mathematics which will enable students to score well in the board examination. The syllabus includes certain challenging concepts like Value Added Tax, Ratio and Proportion, Quadric Equations among others which require effective study materials. Our study materials for ICSE Class 10 consist of video lessons, question banks, sample papers, revision notes and past year papers which improve the quality of learning.

Read  more

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(A)

Question 1

Prove:

Solution 1

Question 2

Prove:

Solution 2

Question 3

Prove:

Solution 3

Question 4

Prove:

Solution 4

Question 5

Prove:

Solution 5

Question 6

Prove:

Solution 6

Question 7

Prove:

Solution 7

Question 8

Prove:

Solution 8

Question 9

Prove:

Solution 9

Question 10

Prove:

Solution 10

Question 11

Prove:

Solution 11

Question 12

Prove:

Solution 12

Question 13

Prove:

Solution 13

Question 14

Prove:

Solution 14

Question 15

Prove:

Solution 15

Question 16

Prove:

Solution 16

Question 17

Prove:

Solution 17

Question 18

Prove:

Solution 18

Question 19

Prove:

Solution 19

Question 20

Prove:

Solution 20

Question 21

Prove:

Solution 21

Question 22

Prove:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 22

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables


Question 23

Prove:

Solution 23

Question 24

Prove:

Solution 24

Question 25

Prove:

Solution 25

Question 26

Prove:

Solution 26

Question 27

Prove:

Solution 27

Question 28

Prove:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 28

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 29

Prove:

Solution 29

Question 30

Prove:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 30

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 31

Prove:

Solution 31

Question 32

Prove:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 32

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 33

Prove:

Solution 33

Question 34

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 34

To prove: Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

  

Question 35

Prove:

Solution 35

Question 36

Prove:

Solution 36

Question 37

Prove:

Solution 37

Question 38

Prove:

Solution 38

Question 39

Prove:

Solution 39

Question 40

Prove:

Solution 40

Question 41

Prove:

Solution 41

Question 42

Prove:

Solution 42

Question 43

Prove:

Solution 43

Question 44

Prove:

Solution 44

Question 45

Prove:

Solution 45

Question 46

Prove:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 46

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 47

Prove:

Solution 47

Question 48

Prove:

Solution 48

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(B)

Question 1

Prove that:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Solution 1

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Question 2

If = m and = n, then prove that x2 + y2 = m2 + n2.

Solution 2

Question 3

If m= and n= , prove that

Solution 3

Question 4

If , prove that

Solution 4

Question 5

If Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablesand Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, prove that Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 5

Given:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

and

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 6

If , prove that

Solution 6

Question 7

If and , show that (m2 + n2) cos2B = n2.

Solution 7

LHS = (m2 + n2) cos2B

Hence, (m2 + n2) cos2B = n2.

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(C)

Question 1

Without using trigonometric tables, show that:

(i)

(ii)

(iii)

Solution 1

(i)

(ii)

(iii)

Question 2

Express each of the following in terms of angles between 0°and 45°:

(i) sin 59°+ tan 63°

(ii) cosec 68°+ cot 72°

(iii)cos 74°+ sec 67°

Solution 2

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 3

Show that:

(i)

(ii)

Solution 3

(i)

(ii)

Question 4

For triangle ABC, show that:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 4

(i) We know that for a triangle Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesABC

 Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables A + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesB + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesC = 180°

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) We know that for a triangle Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesABC

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables A + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesB + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesC = 180°

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesB + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesC = 180° - Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesA

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 5

Evaluate:

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Solution 5

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Question 6

A triangle ABC is right angled at B; find the value of

Solution 6

Since, ABC is a right angled triangle, right angled at B.

So, A + C = 90

Question 7

Find (in each case, given below) the value of x if:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 7

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, x = Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 8

In each case, given below, find the value of angle A, where

(i)

(ii)

Solution 8

(i)

(ii)

Question 9

Prove that:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 9

(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 10

Evaluate :

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 11

Evaluate

sin2 34° + sin2 56° + 2tan 18° tan72° - cot2 30°

Solution 11

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables


Question 12

Without using trigonometrical tables, evaluate:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 12

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(D)

Question 1

Use tables to find sine of:

(i) 21°

(ii) 34° 42'

(iii) 47° 32'

(iv) 62° 57'

(v) 10° 20' + 20° 45'

Solution 1

(i) sin 21o = 0.3584

(ii) sin 34o 42'= 0.5693

(iii) sin 47o 32'= sin (47o 30' + 2') =0.7373 + 0.0004 = 0.7377

(iv) sin 62o 57' = sin (62o 54' + 3') = 0.8902 + 0.0004 = 0.8906

(v) sin (10o 20' + 2045') = sin 30o65' = sin 31o5' = 0.5150 + 0.0012 = 0.5162

Question 2

Use tables to find cosine of:

(i) 2° 4’

(ii) 8° 12’

(iii) 26° 32’

(iv) 65° 41’

(v) 9° 23’ + 15° 54’

Solution 2

(i) cos 2° 4’ = 0.9994 - 0.0001 = 0.9993

(ii) cos 8° 12’ = cos 0.9898

(iii) cos 26° 32’ = cos (26° 30’ + 2’) = 0.8949 - 0.0003 = 0.8946

(iv) cos 65° 41’ = cos (65° 36’ + 5’) = 0.4131 -0.0013 = 0.4118

(v) cos (9° 23’ + 15° 54’) = cos 24° 77’ = cos 25° 17’ = cos (25° 12’ + 5’) = 0.9048 - 0.0006 = 0.9042

Question 3

Use trigonometrical tables to find tangent of:

(i) 37°

(ii) 42° 18'

(iii) 17° 27'

Solution 3

(i) tan 37= 0.7536

(ii) tan 4218' = 0.9099

(iii) tan 17o  27' = tan (1724' + 3') = 0.3134 + 0.0010 = 0.3144

Question 4

Use tables to find the acute angle Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, if the value of sin Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables is:

(i) 0.4848

(ii) 0.3827

(iii) 0.6525

Solution 4

(i) From the tables, it is clear that sin 29o = 0.4848

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables= 29o

(ii) From the tables, it is clear that sin 2230' = 0.3827

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 2230'

(iii) From the tables, it is clear that sin 4042' = 0.6521

sin Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables - sin 40o 42' = 0.6525 -; 0.6521 = 0.0004

From the tables, diff of 2' = 0.0004

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 40o  42' + 2' = 4044'

Question 5

Use tables to find the acute angle Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, if the value of cos Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables is:

(i) 0.9848

(ii) 0.9574

(iii) 0.6885

Solution 5

(i) From the tables, it is clear that cos 10° = 0.9848

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 10°

(ii) From the tables, it is clear that cos 16° 48’ = 0.9573

cos Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables - cos 16° 48’ = 0.9574 - 0.9573 = 0.0001

From the tables, diff of 1’ = 0.0001

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 16° 48’ - 1’ = 16° 47’

(iii) From the tables, it is clear that cos 46° 30’ = 0.6884

cos q - cos 46° 30’ = 0.6885 - 0.6884 = 0.0001

From the tables, diff of 1’ = 0.0002

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 46° 30’ - 1’ = 46° 29’

Question 6

Use tables to find the acute angle Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, if the value of tan q is:

(i) 0.2419

(ii) 0.4741

(iii) 0.7391

Solution 6

(i) From the tables, it is clear that tan 13° 36’ = 0.2419

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 13° 36’

(ii) From the tables, it is clear that tan 25° 18’ = 0.4727

tan Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables - tan 25° 18’ = 0.4741 - 0.4727 = 0.0014

From the tables, diff of 4’ = 0.0014

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 25° 18’ + 4’ = 25° 22’

(iii) From the tables, it is clear that tan 36° 24’ = 0.7373

tan Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables - tan 36° 24’ = 0.7391 - 0.7373 = 0.0018

From the tables, diff of 4’ = 0.0018

Hence, Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables = 36° 24’ + 4’ = 36° 28’

Chapter 21 - Trigonometrical Identities (Including Trigonometrical Ratios of Complementary Angles and Use of Four Figure Trigonometrical Tables) Exercise Ex. 21(E)

Question 1

Prove the following identities:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(viii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ix) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(x) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xiii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xiv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xvi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(xvii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 1

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

(ii)Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(viii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

 

 

 

 

 

(ix) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

(x) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(xi)Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xiii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xiv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xvi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(xvii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Question 2

If Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablesand Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, then prove that:

q(p2 - 1) = 2p

Solution 2

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Question 3

If Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, show that:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Solution 3

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

Question 4

If Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables, show that:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Solution 4

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Question 5

If tan A = n tan B and sin A = m sin B, prove that:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Solution 5

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

Question 6

(i) If 2 sinA - 1 = 0, show that:

sin 3A = 3 sinA - 4 sin3A

(ii) If 4 cos2A - 3 = 0, show that:

cos 3A = 4 cos3A - 3 cosA

 

Solution 6

(i) 2 sinA - 1 = 0

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

Question 7

Evaluate:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(viii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

 

 

Solution 7

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(vi) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(vii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(viii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Question 8

Prove that:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

Solution 8

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Question 9

If A and B are complementary angles, prove that:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iii) cosec2A + cosec2B = cosec2A cosec2B

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Solution 9

Since, A and B are complementary angles, A + B = 90°

(i)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(ii)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

(iii)

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

= cosec2A [sec(90 - B)]2

= cosec2A cosec2B

 

 

 

 

 

 

 

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

 

 

 

 

 

 

Question 10

Prove that:

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

Solution 10

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables




 

 

 

 

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

Question 11

If 4cos2A - 3 = 0 and 0°Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesA Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables90°, then prove that:

(i) sin3A= 3 sinA - 4 sin3A

(ii) cos3A= 4 cos3A - 3 cosA

Solution 11

4 cos2A - 3 = 0

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

 

 

 

 

Question 12

Find A, if 0°Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical TablesA Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables90° and:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(ii) sin 3A - 1 = 0

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Solution 12

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(ii) sin 3A - 1 = 0

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(iii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(iv) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(v) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

Question 13

If 0° < A < 90°; find A, if:

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

Solution 13

(i) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

(ii) Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

 

 

 

 

 

Question 14

Prove that:

(cosec A - sin A) (sec A - cos A) sec2A = tan A

Solution 14

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 15

Prove the identity (sin θ + cos θ) (tan θ + cot θ) = sec θ + cosec θ.

Solution 15

Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Question 16

Evaluate without using trigonometric tables,

sin2 28° + sin2 62° + tan2 38° - cot2 52° + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablessec2 30° 

Solution 16

sin2 28° + sin2 62° + tan2 38° - cot2 52° + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablessec2 30° 

= sin2 28° + [sin (90 - 28)°]2 + tan2 38° - [cot(90 - 38)°]2 + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablessec2 30° 

= sin2 28°  + cos2 28° + tan2 38° - tan2 38° + Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tablessec2 30° 

 Selina Solutions Icse Class 10 Mathematics Chapter - Trigonometrical Identities Including Trigonometrical Ratios Of Complementary Angles And Use Of Four Figure Trigonometrical Tables

Why to choose our study materials for ICSE Class 10 Mathematics?

  • Designed in simple and comprehensive language
  • Contain 285 video lessons, 37 revision notes, 3709+ questions in bank, set of 6 sample papers and 9 past year papers
  • Prepared by subject experts
  • Revised from time to time
  • Useful for doing quick revision
  • Helpful when doing homework