# Solution of Chapter 6. Trigonometric Identities (RD Sharma - Mathematics Book)

## Exercise 6.1

1

Prove the following trigonometric identities:

2

Prove the following trigonometric identities:

3

Prove the following trigonometric identities:

4

Prove the following trigonometric identities:

5

Prove the following trigonometric identities:

6

Prove the following trigonometric identities:

7

Prove the following trigonometric identities:

8

Prove the following trigonometric identities:

9

Prove the following trigonometric identities:

10

Prove the following trigonometric identities:

11

Prove the following trigonometric identities:

12

Prove the following trigonometric identities:

13

Prove the following trigonometric identities:

14

Prove the following trigonometric identities:

15

Prove the following trigonometric identities:

16

Prove the following trigonometric identities:

17

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

19

Prove the following trigonometric identities:

20

Prove the following trigonometric identities:

21

Prove the following trigonometric identities:

22

Prove the following trigonometric identities:

23

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

27

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

30

Prove the following trigonometric identities:

31

Prove the following trigonometric identities:

32

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

34

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

36

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

38

Prove the following trigonometric identities:

39

Prove the following trigonometric identities:

40

Prove the following trigonometric identities:

41

Prove the following trigonometric identities:

42

Prove the following trigonometric identities:

43

Prove the following trigonometric identities:

44

Prove the following trigonometric identities:

45

Prove the following trigonometric identities:

46

Prove the following trigonometric identities:

47

Prove the following trigonometric identities:

47

Prove the following trigonometric identities:

47

Prove the following trigonometric identities:

48

Prove the following trigonometric identities:

49

Prove the following trigonometric identities:

50

Prove the following trigonometric identities:

51

Prove the following trigonometric identities:

52

Prove the following trigonometric identities:

53

Prove the following trigonometric identities:

54

Prove the following trigonometric identities:

55
56

Prove the following trigonometric identities:

57

Prove the following trigonometric identities:

58

Prove the following trigonometric identities:

59

Prove the following trigonometric identities:

60

Prove the following trigonometric identities:

61

Prove the following trigonometric identities:

62

Prove the following trigonometric identities:

63

Prove the following trigonometric identities:

64

Prove the following trigonometric identities:

65

Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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Prove the following trigonometric identities:

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If and prove that

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and , prove that .

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If , , prove that .

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If , , prove that

.

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If , prove that .

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If , prove that .

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If and , prove that

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If and , prove that .

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If , prove that

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Prove that:

(i)

(ii)

(iii)

(iv)

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If , prove that

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Given that:

Show that one of the values of each member of this equality is sin sinsin

86

If prove that

87

If , and , show that

## Exercise 6.2

1

If , find all other trigonometric ratios of angle .

2

If , find all other trigonometric ratios of angle

3

If , find the value of

4

If , find the value of

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If , find the value of

6

If , find the value of

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If , find the value of

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If , find the value of

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If , find the value of

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If , find the value of

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If , find the value of

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If, find .

## CCE - Formative Assessment

1

Define an identity.

2

What is the value of (1 – cos2θ) cosec2θ?

3

What is the value of (1 + cot2θ) sin2θ?

4

What is the value of ?

5

If sec θ + tanθ = x, write the value of sec θ tan θ in terms of x.

6

If cosec θ cot θ = α, write the value of cosec θ + cot α.

7

Write the value of cosec2 (90° θ) tan2θ.

8

Write the value of sin A cos (90° A) + cos A sin (90° A).

9

Write the value of .

10

If x = a sin θ and y = b cos θ, what is the value of b2x2 + a2y2 ?

11

If , what is the value of cot θ + cosec θ?

12

What is the value of 9 cot2θ 9 cosec2θ?

13

What is the value of ?

14

What is the value of ?

15

What is the value of (1 + tan2θ) (1 sin θ) (1 + sin θ)?

16

If , find the value of tan A + cot A.

17

If , then find the value of 2 cot2θ + 2.

18

If , then find the value of 9 tan2θ + 9.

19

If sec2θ (1 + sin θ) (1 sin θ) = k, then find the value of k.

20

If cosec2θ (1 + cos θ) (1 cos θ) = λ, then find the value of λ.

21

If sin2θ cos2θ (1 + tan2θ) (1 + cot2θ) = λ, then find the value of λ.

22

If 5x = sec θ and , find the value of .

23

If cosec θ = 2x and , find the value of

1

If sec θ + tan θ = x, then sec θ =

2

If sec θ + tan θ = x, then tan θ =

3

is equal to

4

The value of is

5

sec4 A sec2 A is equal to

6

cos4 A sin4 A is equal to

7

is equal to

8

is equal to

9

The value of (1 + cot θ cosec θ) (1 + tan θ + sec θ) is

10

is equal to

11

(cosec θ sin θ) (sec θ cos θ) (tan θ + cot θ) is equal

12

If x = a cos θ and y = b sin θ, then b2x2 + a2y2 =

13

If x = a sec θ and y = b tan θ, then b2x2 a2y2 =

14

is equal to

15

2(sin6θ + cos6θ) 3(sin4θ + cos4θ) is equal to

16

If a cos θ + b sin θ and a sin θ b cos θ = 3, then a2 + b2 =

17

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p2 q2 =

18

The value of sin2 29° + sin2 61° is

19

If x = r sin θ cos φ, y = r sin θ sin φ and z = r cos θ, then

20

If sin θ + sin2 = 1, then cos2θ + cos4θ =

21

If a cos θ + b sin θ = m and a sin θ b cos θ = n, then a2 + b2 =

22

If cos A + cos2 A = 1, then sin2 A + sin4 A

23

If x = a sec θ cos φ, y = b sec θ sin φ and z = c tan θ, then

24

If a cos θ b sin θ = c, then a sin θ + b cos θ =

25

9 sec2 A 9 tan2 A is equal to

26

(1 + tan θ + sec θ) (1 + cot θ cosec θ) =