RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2

RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2

These Solutions are part of RD Sharma Class 10 Solutions. Here we have given RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2

Other Exercises

Evaluate each of the following (1-19) : 1.
Question 1.
sin45° sin30° + cos45° cos30°.
Solution:
sin 45° sin 30° + cos 45° cos 30°
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 1

Question 2.
sin60° cos30° + cos60° sin30°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 2

Question 3.
cos60° cos45° – sin60° sin45°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 3

Question 4.
sin230° + sin245° + sin260° + sin2290°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 4

Question 5.
cos230° + cos245° + cos260° + cos290°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 5
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 6

Question 6.
tan230° + tan260° + tan245°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 7

Question 7.
2sin230° – 3cos245° + tan260°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 8

Question 8.
sin230°cos24S° + 4tan230° + \(\frac { 1 }{ 2 }\) sin290° -2cos290° + \(\frac { 1 }{ 24 }\) cos20°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 9
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 10

Question 9.
4 (sin4 60° + cos4 30°) – 3 (tan2 60° – tan2 45°) + 5cos2 45°
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 11

Question 10.
(cosecc2 45° sec2 30°) (sin2 30° + 4cot2 45° – sec2 60°).
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 12
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 13

Question 11.
cosec3 30° cos 60° tan3 45° sin2 90° sec2 45° cot 30°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 14

Question 12.
cot2 30° – 2cocs2 60° – \(\frac { 3 }{ 4 }\)sec2 45° – 4sec2 30°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 15

Question 13.
(cos0° + sin45° + sin30°) (sin90° – cos45° + cos60°)
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 16
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 17

Question 14.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 18
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 19

Question 15.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 20
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 21

Question 16.
4 (sin4 30° + cos2 60°) – 3 (cos2 45° – sin2 90°) – sin2 60°
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 22

Question 17.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 23
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 24

Question 18.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 25
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 26
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 27

Question 19.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 28
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 29

Find the value of x in each of the following : (20-25)

Question 20.
2sin 3x = √3
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 30

Question 21.
2sin \(\frac { x }{ 2 }\) = 1
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 31

Question 22.
√3 sin x=cos x
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 32

Question 23.
tan x = sin 45° cos 45° + sin 30°
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 33

Question 24.
√3 tan 2x = cos 60° +sin 45° cos 45°
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 34
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 35

Question 25.
cos 2x = cos 60° cos 30° + sin 60° sin 30°
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 36

Question 26.
If θ = 30°, verify that :
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 37
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 38
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 39
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 40
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 41

Question 27.
If A = B = 60°, verify that:
(i) cos (A – B) = cos A cos B + sin A sin B
(ii) sin (A – B) = sin A cos B – cos A sin B tan A – tan B
(iii) tan (A – B) = \(\frac { tanA-tanB }{ 1+tanA-tanB }\)
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 42
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 43

Question 28.
If A = 30° and B = 60°, verify that :
(i) sin (A + B) = sin A cos B + cos A sin B
(ii) cos (A + B) = cos A cos B – sin A sin B
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 44

Question 29.
If sin (A + B) = 1 and cos (A,-B) = 1,0° < A + B < 90°, A > B find A and B.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 45
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 46

Question 30.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 47
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 48

Question 31.
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 49
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 50
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 51

Question 32.
In a ∆ABC right angle at B, ∠A = ∠C. Find the values of
(i) sin A cos C + cos A sin C
(ii) sin A sin B + cos A cos B
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 52

Question 33.
Find acute angles A and B, if sin (A + 2B)=\(\frac { \sqrt { 3 } }{ 2 }\) and cos (A + 4B) = 0, A > B.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 53

Question 34.
In ΔPQR, right-angled at Q, PQ = 3 cm and PR = 6 cm. Determine ∠P and ∠R.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 54
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 55

Question 35.
If sin (A – B) = sin A cos B – cos A sin B and cos (A – B) = cos A cos B + sin A sin B, find the values of sin 15° and cos 15°.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 56

Question 36.
In a right triangle ABC, right angled at ∠C if ∠B = 60° and AB – 15 units. Find the remaining angles and sides.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 57
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 58

Question 37.
If ΔABC is a right triangle such that ∠C = 90°, ∠A = 45° and BC = 7 units. Find ∠B, AB and AC.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 59
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 60

Question 38.
In a rectangle ABCD, AB = 20 cm, ∠BAC = 60°, calculate side BC and diagonals AC and BD.
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 61

Question 39.
If A and B are acute angles such that
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 62
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 63
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 64

Question 40.
Prove that (√3 + 1) (3 – cot 30°) = tan3 60° – 2sin 60°. [NCERT Exemplar]
Solution:
RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 65

Hope given RD Sharma Class 10 Solutions Chapter 10 Trigonometric Ratios Ex 10.2 are helpful to complete your math homework.

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