1

Prove the following trigonometric identities:

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2

Prove the following trigonometric identities:

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3

Prove the following trigonometric identities:

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4

Prove the following trigonometric identities:

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5

Prove the following trigonometric identities:

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6

Prove the following trigonometric identities:

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7

Prove the following trigonometric identities:

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8

Prove the following trigonometric identities:

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9

Prove the following trigonometric identities:

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10

Prove the following trigonometric identities:

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11

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Prove the following trigonometric identities:

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12

Prove the following trigonometric identities:

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13

Prove the following trigonometric identities:

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14

Prove the following trigonometric identities:

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15

Prove the following trigonometric identities:

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16

Prove the following trigonometric identities:

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17

Prove the following trigonometric identities:

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18

Prove the following trigonometric identities:

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19

Prove the following trigonometric identities:

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20

Prove the following trigonometric identities:

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21

Prove the following trigonometric identities:

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22

Prove the following trigonometric identities:

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23

Prove the following trigonometric identities:

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23

Prove the following trigonometric identities:

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24

Prove the following trigonometric identities:

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25

Prove the following trigonometric identities:

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26

Prove the following trigonometric identities:

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27

Prove the following trigonometric identities:

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28

Prove the following trigonometric identities:

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29

Prove the following trigonometric identities:

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30

Prove the following trigonometric identities:

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31

Prove the following trigonometric identities:

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32

Prove the following trigonometric identities:

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33

Prove the following trigonometric identities:

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34

Prove the following trigonometric identities:

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35

Prove the following trigonometric identities:

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36

Prove the following trigonometric identities:

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37

Prove the following trigonometric identities:

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38

Prove the following trigonometric identities:

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39

Prove the following trigonometric identities:

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40

Prove the following trigonometric identities:

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41

Prove the following trigonometric identities:

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42

Prove the following trigonometric identities:

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43

Prove the following trigonometric identities:

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44

Prove the following trigonometric identities:

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45

Prove the following trigonometric identities:

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46

Prove the following trigonometric identities:

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47

Prove the following trigonometric identities:

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47

Prove the following trigonometric identities:

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47

Prove the following trigonometric identities:

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48

Prove the following trigonometric identities:

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49

Prove the following trigonometric identities:

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50

Prove the following trigonometric identities:

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51

Prove the following trigonometric identities:

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52

Prove the following trigonometric identities:

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53

Prove the following trigonometric identities:

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54

Prove the following trigonometric identities:

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55

If prove that

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56

Prove the following trigonometric identities:

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57

Prove the following trigonometric identities:

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58

Prove the following trigonometric identities:

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59

Prove the following trigonometric identities:

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60

Prove the following trigonometric identities:

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61

Prove the following trigonometric identities:

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62

Prove the following trigonometric identities:

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63

Prove the following trigonometric identities:

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64

Prove the following trigonometric identities:

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65

Prove the following trigonometric identities:

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66

Prove the following trigonometric identities:

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67

Prove the following trigonometric identities:

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68

Prove the following trigonometric identities:

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69

Prove the following trigonometric identities:

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70

Prove the following trigonometric identities:

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71

Prove the following trigonometric identities:

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72

Prove the following trigonometric identities:

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73

Prove the following trigonometric identities:

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74

If and prove that

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75

and , prove that .

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76

If , , prove that .

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77

If , , prove that

.

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78

If , prove that .

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If , prove that .

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80

If and , prove that

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81

If and , prove that .

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82

If , prove that

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83

Prove that:

(i)

(ii)

(iii)

(iv)

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84

If , prove that

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85

Given that:

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

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86

If prove that

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87

If , and , show that

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1

If , find all other trigonometric ratios of angle .

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2

If , find all other trigonometric ratios of angle

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3

If , find the value of

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4

If , find the value of

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5

If , find the value of

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6

If , find the value of

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7

If , find the value of

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8

If , find the value of

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9

If , find the value of

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10

If , find the value of

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11

If , find the value of

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12

If, find .

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1

Define an identity.

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2

What is the value of (1 – cos^{2}θ) cosec^{2}θ?

3

What is the value of (1 + cot^{2}θ) sin^{2}θ?

4
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5

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

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6

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

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7

Write the value of cosec^{2} (90° − θ) − tan^{2}θ.

8

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

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9

Write the value of .

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10

If x = a sin θ and y = b cos θ, what is the value of b^{2}x^{2} + a^{2}y^{2} ?

11

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

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12

What is the value of 9 cot^{2}θ − 9 cosec^{2}θ?

13

What is the value of ?

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14

What is the value of ?

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15

What is the value of (1 + tan^{2}θ) (1 − sin θ) (1 + sin θ)?

16

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

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17

If , then find the value of 2 cot^{2}θ + 2.

18

If , then find the value of 9 tan^{2}θ + 9.

19

If sec^{2}θ (1 + sin θ) (1 − sin θ) = k, then find the value of k.

20

If cosec^{2}θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.

21

If sin^{2}θ cos^{2}θ (1 + tan^{2}θ) (1 + cot^{2}θ) = λ, then find the value of λ.

22

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

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23

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

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1

If sec θ + tan θ = x, then sec θ =

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2

If sec θ + tan θ = x, then tan θ =

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3

is equal to

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4

The value of is

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5

sec^{4} A − sec^{2} A is equal to

6

cos^{4} A − sin^{4} A is equal to

7

is equal to

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8

is equal to

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9

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

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10

is equal to

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11

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

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12

If x = a cos θ and y = b sin θ, then b^{2}x^{2} + a^{2}y^{2} =

13

If x = a sec θ and y = b tan θ, then b^{2}x^{2}− a^{2}y^{2} =

14

is equal to

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15

2(sin^{6}θ + cos^{6}θ) − 3(sin^{4}θ + cos^{4}θ) is equal to

16

If a cos θ + b sin θ and a sin θ − b cos θ = 3, then a^{2} + b^{2} =

17

If a cot θ + b cosec θ = p and b cot θ + a cosec θ = q, then p^{2}− q^{2} =

18

The value of sin^{2} 29° + sin^{2} 61° is

19

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

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20

If sin θ + sin^{2} = 1, then cos^{2}θ + cos^{4}θ =

21

If a cos θ + b sin θ = m and a sin θ − b cos θ = n, then a^{2} + b^{2} =

22

If cos A + cos^{2} A = 1, then sin^{2} A + sin^{4} A

23

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

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24

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

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25

9 sec^{2} A − 9 tan^{2} A is equal to

26

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

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27

(sec A + tan A) (1 − sin A) =

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27

is equal to

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