RD Sharma - Mathematics

Book: RD Sharma - Mathematics

Chapter: 6. Trigonometric Identities

Subject: Maths - Class 10th

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Chapter Exercises

Exercise 6.1
Exercise 6.2
CCE - Formative Assessment

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:
18

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:
23

Prove the following trigonometric identities:
24

Prove the following trigonometric identities:
25

Prove the following trigonometric identities:
26

Prove the following trigonometric identities:
27

Prove the following trigonometric identities:
28

Prove the following trigonometric identities:
29

Prove the following trigonometric identities:
30

Prove the following trigonometric identities:
31

Prove the following trigonometric identities:
32

Prove the following trigonometric identities:
33

Prove the following trigonometric identities:
34

Prove the following trigonometric identities:
35

Prove the following trigonometric identities:
36

Prove the following trigonometric identities:
37

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

If prove that
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:
66

Prove the following trigonometric identities:
67

Prove the following trigonometric identities:
68

Prove the following trigonometric identities:
69

Prove the following trigonometric identities:
70

Prove the following trigonometric identities:
71

Prove the following trigonometric identities:
72

Prove the following trigonometric identities:
73

Prove the following trigonometric identities:
74

If and prove that

75

and , prove that .
76

If , , prove that .
77

If , , prove that

.
78

If , prove that .
79

If , prove that .
80

If and , prove that

81

If and , prove that .
82

If , prove that
83

Prove that:

(i)


(ii)


(iii)


(iv)

84

If , prove that
85

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

5

If , find the value of

6

If , find the value of

7

If , find the value of

8

If , find the value of

9

If , find the value of

10

If , find the value of

11

If , find the value of

12

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) =
27

(sec A + tan A) (1 − sin A) =
27

is equal to