FRANK Solutions for Class 9 Maths Chapter 27 - Trigonometrical Ratios of Standard Angles

Complete your revision more effectively with Frank Solutions for ICSE Class 9 Mathematics Chapter 27 Trigonometrical ratios of standard angles. Check out the answers by experts to understand how they have provided proofs or presented an evaluation of trigonometric ratios given in the Frank textbook questions. The expert solutions on TopperLearning can be accessed 24x7 online.

In addition, the Frank solutions for Chapter 27 also provide elaborate answers on finding the angle or side of a triangle using trigonometry. To further revise this ICSE Class 9 Maths chapter or chapters from other syllabus, take a look at our Selina textbook solutions, doubts and solutions, solved question papers, and other useful resources.

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Chapter 27 - Trigonometrical Ratios of Standard Angles Exercise Ex. 27.1

Question 1
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Solution 1
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 2
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Solution 2
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 3(a)

Prove that :

sin 60° .cos 30° - sin 60°. sin 30° =Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(b)

Prove that :

cos 60° . cos 30° - sin 60° . sin 30° = 0

Solution 3(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(c)

Prove that :

sec245° - tan245° = 1

Solution 3(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(d)

Prove that :

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(a)

Find the value of 'A', if

2 cos A = 1

Solution 4(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(b)

Find the value of 'A', if

2 sin 2A = 1

Solution 4(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(c)

Find the value of 'A', if

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 4(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(d)

Find the value of 'A', if

2 cos 3A = 1

Solution 4(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(e)

Find the value of 'A', if

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 4(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(f)

Find the value of 'A', if

cot 3A = 1

Solution 4(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(a)

Find the value of 'A', if

(1 - cosec A)(2 - sec A) = 0

Solution 5(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(b)

Find the value of 'A', if

(2 - cosec 2A) cos 3A = 0

Solution 5(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 6

If sin α + cosβ = 1 and α= 90°, find the value of 'β'.

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 7(a)

Solve for 'Ө':

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 7(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 7(b)

Solve for 'Ө':

cot2(Ө - 5)° = 3

Solution 7(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 7(c)

Solve for 'Ө':

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 7(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 8

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 9

If sin Ө = cosӨ and 0° < Ө<90°, find the value of 'Ө'.

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 10

If tan Ө= cot Ө and 0°≤Ө≤ 90°, find the value of 'Ө'.

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(a)

If Ө = 30°, verify that:Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 12(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(b)

If Ө = 30°, verify that:Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 12(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(c)

If A = 30°, verify that:Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 12(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(d)

If Ө = 30°, verify that:

sin 3Ө = 4sin Ө.sin(60° - Ө) sin(60° + Ө)

Solution 12(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(e)

If Ө = 30°, verify that:

1 - sin 2Ө= (sin Ө - cosӨ)2

Solution 12(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 13(a)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 13(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 13(b)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 13(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 14

If Ө = 15°, find the value of:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Anglescos 3Ө - sin 6Ө + 3sin (5Ө + 15°) - 2 tan23Ө

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 16(a)

If A = 30° and B = 60°, verify that:

sin (A + B) = sin A cos B + cos A sin B

Solution 16(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 16(b)

If A = 30° and B = 60°, verify that:

cos (A + B) = cos A cos B - sin A sin B

Solution 16(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 16(c)

If A = 30° and B = 60°, verify that:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 16(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 16(d)

If A = 30° and B = 60°, verify that:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 16(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 17(a)

If A = B = 45°, verify that

sin (A - B) = sin A .cos B - cos A.sin B

Solution 17(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 17(b)

If A = B = 45°, verify that

cos (A - B) = cosA.cos B + sin A.sin B

Solution 17(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 18

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 19(a)

If Ө < 90°, find the value of:

sin2Ө + cos2Ө

Solution 19(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 19(b)

If Ө < 90°, find the value of:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 19(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 20(a)

IfFrank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Anglessec 2Ө = 2 and Ө< 90°, find the value of

Ө

Solution 20(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 20(b)

IfFrank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Anglessec 2Ө = 2 and Ө< 90°, find the value of

cos 3Ө

Solution 20(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 20(c)

IfFrank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Anglessec 2Ө = 2 and Ө< 90°, find the value of

cos2 (30° + Ө) + sin2 (45° - Ө)

Solution 20(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 21

In the given figure, PQ = 6 cm, RQ = x cm and RP = 10 cm, find

a. cosӨ

b. sin2 Ө - cos2Ө

c. Use tan Ө to find the value of RQ

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 21

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 22

Find the value of:Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

If 3 tan2Ө - 1 = 0, find the value

a. cos 2Ө

b. sin 2Ө

Solution 22

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 23

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 23

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 24

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 24

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 25

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 25

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 26

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 26

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 27

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 27

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Chapter 27 - Trigonometrical Ratios of Standard Angles Exercise Ex. 27.2

Question 14

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 14

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 15

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 15

2Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 16

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 16

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles
Question 1(a)

Find the value of 'x' in each of the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(a)

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 1(b)

Find the value of 'x' in each of the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 1(c)

Find the value of 'x' in each of the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(d)

Find the value of 'x' in each of the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2

Find the length of AD.

Given: ABC = 60°, DBC = 45° and BC = 24 cm.

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 2

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3

Find lengths of diagonals AC and BD. Given AB = 24 cm and BAD = 60°.

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4

In a trapezium ABCD, as shown, ABDC, AD = DC = BC = 24 cm and A = 30°. Find:

length of AB

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles 

Solution 4

 

Construction: Draw DP AB and CM AB

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5

Find the length of EC.

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Solution 5

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 6

In the given figure, AB and EC are parallel to each other. Sides AD and BC are 1.5 cm each and are perpendicular to AB. Given that AED = 45° and ACD = 30°. Find:

a. AB

b. AC

c. AE

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 7

In the given figure, B = 60°, C = 30°, AB = 8 cm and BC = 24 cm. Find:

a. BE

b. AC

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 7

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 8

Find:

a. BC

b. AD

c. AC

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 9(a)

Find the value 'x', if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 9(b)

Find the value 'x', if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 9(c)

Find the value 'x', if:Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 9(d)

Find the value 'x', if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 9(e)

Find the value 'x', if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles 

Question 9(f)

Find the value 'x', if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 9(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 10(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 10(a)

Construction: Draw BX AE

Then, BD = EX = 14 cm and BX = ED

AX = AE - EX = 16 - 14 = 2

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 10(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Solution 10(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 12(a)

Find x and y, in each of the following figure:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Solution 12(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12(b)

Find x and y, in each of the following figure:

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 12(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 13

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 17

In right-angled triangle ABC; B = 90°. Find the magnitude of angle A, if:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 17

Consider the following figure,

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 18

A ladder is placed against a vertical tower. If the ladder makes an angle of 30° with the ground and reaches upto a height of 18 m of the tower; find length of the ladder.

Solution 18

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 19

The perimeter of a rhombus is 100 cm and obtuse angle of it is 120°. Find the lengths of its diagonals.

Solution 19

Consider the following figure,

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Question 20

In the given figure; B = 90°, ADB = 30°, ACB = 45° and AB = 24 m.

Find the length of CD.

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 20

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 21

In the given figure, a rocket is fired vertically upwards from its launching pad P. It first rises 20 km vertically upwards and then 20 km at 60° to the vertical. PQ represents the first stage of the journey and QR the second. S is a point vertically below R on the horizontal level as P, find:

a. the height of the rocket when it is at point R.

b. the horizontal distance of point S from P.

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 21

Draw QM RS.

Clearly, RQM = 30°  

 

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

 

Chapter 27 - Trigonometrical Ratios of Standard Angles Exercise Ex. 27.3

Question 1(a)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(b)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(c)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(d)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(e)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 1(f)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 1(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(a)

Evaluate the following:

sin 31° - cos 59°

Solution 2(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(b)

Evaluate the following:

cot 27° - tan 63°

Solution 2(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(c)

Evaluate the following:

cosec 54° - sec 36°

Solution 2(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(d)

Evaluate the following:

sin 28° sec 62° + tan 49° tan 41°

Solution 2(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(e)

Evaluate the following:

sec 16° tan 28° - cot 62° cosec 74°

Solution 2(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 2(f)

Evaluate the following:

sin 22° cos 44° - sin 46° cos 68°

Solution 2(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(a)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(b)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(c)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 3(d)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 3(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(a)

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

sin 65° + cot 59°

Solution 4(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(b)

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

cos 72° - cos 88°

Solution 4(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(c)

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

cosec 64° + sec 70°

Solution 4(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(d)

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

tan 77° - cot 63° + sin 57°

Solution 4(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(e)

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

sin 53° + sec 66° - sin 50°

Solution 4(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 4(f)

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

cos 84° + cosec 69° - cot 68°

Solution 4(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(a)

Evaluate the following:

sin 35° sin 45° sec 55° sec 45°

Solution 5(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(b)

Evaluate the following:

cot 20° cot 40° cot 45° cot 50° cot 70°

Solution 5(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(c)

Evaluate the following:

cos 39° cos 48° cos 60° cosec 42° cosec 51°

Solution 5(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(d)

Evaluate the following:

sin (35° + Ө) - cos (55° - Ө) - tan (42° + Ө) + cot (48° - Ө)

Solution 5(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(e)

Evaluate the following:

tan (78° + Ө) + cosec (42° + Ө) - cot (12° - Ө) - sec(48° - Ө)

Solution 5(e)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(f)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 5(f)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(g)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 5(g)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(h)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 5(h)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(i)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 5(i)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 5(j)

Evaluate the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 5(j)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 6

If cos 3Ө = sin (Ө - 34°), find the value of Ө if 3Ө is an acute angle.

Solution 6

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 7

If tan 4Ө = cot (Ө + 20°), find the value of Ө if 4Ө is an acute angle.

Solution 7

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 8

If sec 2Ө = cosec 3Ө, find the value of Ө if it is known that both 2Ө and 3Ө are acute angles.

Solution 8

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 9

If sin (Ө - 15°) = cos (Ө - 25°), find the value of Ө if (Ө -15°) and (Ө - 25°) are acute angles.

Solution 9

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 10

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 10

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 11

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 12

If cosӨ = sin 60° and Ө is an acute angle find the value of 1- 2 sin2Ө

Solution 12

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 13

If sec Ө = cosec 30° and Ө is an acute angle, find the value of 4 sin2Ө - 2 cos2Ө.

Solution 13

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 14(a)

Prove the following:

tan Ө tan (90° - Ө) = cot Ө cot (90° - Ө)

Solution 14(a)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 14(b)

Prove the following:

sin 58° sec 32° + cos 58° cosec 32° = 2

Solution 14(b)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 14(c)

Prove the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 14(c)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 14(d)

Prove the following:

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 14(d)

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Question 15

If A + B = 90°, prove that

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles

Solution 15

Frank Solutions Icse Class 9 Mathematics Chapter - Trigonometrical Ratios Of Standard Angles