Chapter 25 : Complementary Angles - Selina Solutions for Class 9 Maths ICSE

Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.

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Chapter 25 - Complementary Angles Excercise Ex. 25

Question 1

Solution 1

  

Question 2

Solution 2

  

Question 3

Solution 3

  

Question 4

Solution 4

  

Question 5

Evaluate colon
sin squared 40 to the power of straight o minus cos squared 50 to the power of straight o

Solution 5

sin squared space 40 degree minus cos squared space 50
equals sin squared space left parenthesis 90 degree minus 50 degree right parenthesis minus cos squared space 50 degree
equals cos squared space 50 degree minus cos squared space 50 degree
equals 0

Question 6

Solution 6

  

Question 7

Solution 7

  

Question 8

Solution 8

  

Question 9

Solution 9

  

Question 10

Solution 10

Question 11

Solution 11

Question 12

Solution 12

  

Question 13

Solution 13

  

Question 14

Solution 14

  

Question 15

Show that:

tan 10° tan 15° tan 75° tan 80° = 1

Solution 15

L.H.S.

= tan 10° tan 15° tan 75° tan 80°

= tan (90° - 80°) tan (90° - 75°) tan 75° tan 80°

= cot 80° cot 75 ° tan 75° tan 80°

= (cot 80° tan 80°)(cot 75° tan 75°)

= (1)(1)

= 1

= R.H.S.

Question 16

Show that:

sin 42° sec 48° + cos 42° cosec 48° = 2

Solution 16

   

Question 17

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 17

Question 18

For triangle ABC, show that:

(i)

(ii)

Solution 18

(i) We know that for a triangle ABC

 A + B + C = 180°

(ii) We know that for a triangle ABC

A + B + C = 180°

B + C = 180° - A

Question 19

Evaluate:

(i)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

(ix)

Solution 19

(i)


left parenthesis ii right parenthesis space space 3 cos space 80 degree space cosec space 10 degree plus 2 sin space 59 degree space sec space 31 degree
equals 3 cos space left parenthesis 90 degree minus 10 degree right parenthesis space cosec space 10 degree plus 2 sin space left parenthesis 90 degree minus 31 right parenthesis space sec space 31 degree
equals 3 sin space 10 degree cosec space 10 degree plus 2 cos space 31 degree space sec space 31 degree
equals 3 cross times 1 plus 2 cross times 1
equals 3 plus 2
equals 5

 

(iii)

 

(iv)

 

(v)

 

(vi)

 

(vii)

 

(viii)

 

(ix)

Question 20

Solution 20

  

Question 21

In each case, given below, find the value of angle A, where 0° A 90°.

sin (90° - 3A).cosec 42° = 1

Solution 21

Question 22

In each case, given below, find the value of angle A, where 0° A 90°.

cos (90° - A).sec 77° = 1

Solution 22

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