EduSahara™ Worksheet

EduSahara™ Assignment

Name : Trigonometric ratios in terms of other ratios

Chapter : Trigonometrical Identities

Grade : ICSE Grade X

License : Non Commercial Use

Question 1

1.

Express
sin

θ
in terms of
cos

θ

(i)

1

cos

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

√

1

−

cos

2

θ
(iv)

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

cos

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

1

tan

θ
(iv)

√

1

+

tan

2

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

√

1

+

cot

2

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

1

√

1

+

cot

2

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

1

sec

θ
(ii)

1

√

sec

2

θ

−

1

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

√

sec

2

θ

−

1

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

1

√

cosec

2

θ

−

1
(iv)

√

cosec

2

θ

−

1
(v)

1

cosec

θ

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

1

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ
(v)

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

tan

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

1

√

1

+

cot

2

θ
(iii)

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

cot

θ

√

1

+

cot

2

θ

Question 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

1

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

1

sec

θ

Question 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

1

cosec

θ
(iii)

√

cosec

2

θ

−

1

(iv)

√

cosec

2

θ

−

1

cosec

θ

(v)

1

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ
(ii)

1

sin

θ
(iii)

1

√

1

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ
(ii)

1

cos

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

1

√

1

−

cos

2

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

√

1

+

cot

2

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

1

√

1

+

cot

2

θ
(v)

1

cot

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

1

√

sec

2

θ

−

1

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

1

sec

θ
(v)

√

sec

2

θ

−

1

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1
(ii)

1

cosec

θ

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

1

√

cosec

2

θ

−

1

Question 16

16.

Express
cot

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ
(iii)

1

√

1

−

sin

2

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

1

sin

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ
(ii)

1

cos

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

√

1

−

cos

2

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 18

18.

Express
cot

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ
(ii)

1

√

1

+

tan

2

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

1

tan

θ
(v)

√

1

+

tan

2

θ

Question 19

19.

Express
cot

θ
in terms of
sec

θ

(i)

1

sec

θ
(ii)

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

1

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1
(iii)

1

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 21

21.

Express
sec

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ
(ii)

1

√

1

−

sin

2

θ
(iii)

1

sin

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

√

1

−

cos

2

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

1

cos

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

1

tan

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ

(ii)

√

1

+

cot

2

θ

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ
(v)

1

cot

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1
(v)

1

cosec

θ

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

1

sin

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

√

1

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

1

√

1

−

sin

2

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

1

cos

θ

Question 28

28.

Express
cosec

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

√

1

+

tan

2

θ
(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

tan

θ

Question 29

29.

Express
cosec

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

1

cot

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

1

sec

θ
(iii)

1

√

sec

2

θ

−

1

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

Question 31

31.

Express
sin

58°
in terms of
cos

58°

(i)

cos

58°

√

1

−

cos

2

58°

(ii)

1

√

1

−

cos

2

58°
(iii)

1

cos

58°

(iv)

√

1

−

cos

2

58°

cos

58°

(v)

√

1

−

cos

2

58°

Question 32

32.

Express
sin

49°
in terms of
tan

49°

(i)

√

1

+

tan

2

49°

tan

49°

(ii)

1

tan

49°
(iii)

1

√

1

+

tan

2

49°

(iv)

tan

49°

√

1

+

tan

2

49°

(v)

√

1

+

tan

2

49°

Question 33

33.

Express
sin

63°
in terms of
cot

63°

(i)

1

cot

63°

(ii)

√

1

+

cot

2

63°

cot

63°

(iii)

√

1

+

cot

2

63°

(iv)

cot

63°

√

1

+

cot

2

63°

(v)

1

√

1

+

cot

2

63°

Question 34

34.

Express
sin

48°
in terms of
sec

48°

(i)

√

sec

2

48°

−

1

(ii)

√

sec

2

48°

−

1

sec

48°

(iii)

sec

48°

√

sec

2

48°

−

1

(iv)

1

sec

48°
(v)

1

√

sec

2

48°

−

1

Question 35

35.

Express
sin

67°
in terms of
cosec

67°

(i)

cosec

67°

√

cosec

2

67°

−

1

(ii)

√

cosec

2

67°

−

1

cosec

67°

(iii)

1

cosec

67°
(iv)

√

cosec

2

67°

−

1
(v)

1

√

cosec

2

67°

−

1

Question 36

36.

Express
cos

39°
in terms of
sin

39°

(i)

√

1

−

sin

2

39°

sin

39°

(ii)

√

1

−

sin

2

39°
(iii)

1

sin

39°

(iv)

sin

39°

√

1

−

sin

2

39°

(v)

1

√

1

−

sin

2

39°

Question 37

37.

Express
cos

30°
in terms of
tan

30°

(i)

1

tan

30°

(ii)

√

1

+

tan

2

30°

tan

30°

(iii)

√

1

+

tan

2

30°
(iv)

1

√

1

+

tan

2

30°

(v)

tan

30°

√

1

+

tan

2

30°

Question 38

38.

Express
cos

76°
in terms of
cot

76°

(i)

√

1

+

cot

2

76°

cot

76°

(ii)

√

1

+

cot

2

76°
(iii)

1

√

1

+

cot

2

76°

(iv)

cot

76°

√

1

+

cot

2

76°

(v)

1

cot

76°

Question 39

39.

Express
cos

58°
in terms of
sec

58°

(i)

sec

58°

√

sec

2

58°

−

1

(ii)

√

sec

2

58°

−

1

(iii)

√

sec

2

58°

−

1

sec

58°

(iv)

1

sec

58°
(v)

1

√

sec

2

58°

−

1

Question 40

40.

Express
cos

64°
in terms of
cosec

64°

(i)

√

cosec

2

64°

−

1

cosec

64°

(ii)

cosec

64°

√

cosec

2

64°

−

1

(iii)

1

√

cosec

2

64°

−

1
(iv)

1

cosec

64°
(v)

√

cosec

2

64°

−

1

Question 41

41.

Express
tan

55°
in terms of
sin

55°

(i)

sin

55°

√

1

−

sin

2

55°

(ii)

√

1

−

sin

2

55°
(iii)

1

sin

55°
(iv)

1

√

1

−

sin

2

55°

(v)

√

1

−

sin

2

55°

sin

55°

Question 42

42.

Express
tan

58°
in terms of
cos

58°

(i)

√

1

−

cos

2

58°
(ii)

1

√

1

−

cos

2

58°
(iii)

1

cos

58°

(iv)

√

1

−

cos

2

58°

cos

58°

(v)

cos

58°

√

1

−

cos

2

58°

Question 43

43.

Express
tan

46°
in terms of
cot

46°

(i)

1

cot

46°
(ii)

1

√

1

+

cot

2

46°

(iii)

cot

46°

√

1

+

cot

2

46°

(iv)

√

1

+

cot

2

46°

cot

46°

(v)

√

1

+

cot

2

46°

Question 44

44.

Express
tan

76°
in terms of
sec

76°

(i)

√

sec

2

76°

−

1
(ii)

1

√

sec

2

76°

−

1

(iii)

sec

76°

√

sec

2

76°

−

1

(iv)

√

sec

2

76°

−

1

sec

76°

(v)

1

sec

76°

Question 45

45.

Express
tan

54°
in terms of
cosec

54°

(i)

1

cosec

54°

(ii)

√

cosec

2

54°

−

1

cosec

54°

(iii)

√

cosec

2

54°

−

1
(iv)

1

√

cosec

2

54°

−

1

(v)

cosec

54°

√

cosec

2

54°

−

1

Question 46

46.

Express
cot

25°
in terms of
sin

25°

(i)

√

1

−

sin

2

25°

sin

25°

(ii)

1

√

1

−

sin

2

25°
(iii)

1

sin

25°
(iv)

√

1

−

sin

2

25°

(v)

sin

25°

√

1

−

sin

2

25°

Question 47

47.

Express
cot

80°
in terms of
cos

80°

(i)

1

cos

80°
(ii)

√

1

−

cos

2

80°

(iii)

√

1

−

cos

2

80°

cos

80°

(iv)

cos

80°

√

1

−

cos

2

80°

(v)

1

√

1

−

cos

2

80°

Question 48

48.

Express
cot

20°
in terms of
tan

20°

(i)

√

1

+

tan

2

20°

tan

20°

(ii)

1

tan

20°

(iii)

tan

20°

√

1

+

tan

2

20°

(iv)

1

√

1

+

tan

2

20°
(v)

√

1

+

tan

2

20°

Question 49

49.

Express
cot

27°
in terms of
sec

27°

(i)

√

sec

2

27°

−

1

(ii)

√

sec

2

27°

−

1

sec

27°

(iii)

sec

27°

√

sec

2

27°

−

1

(iv)

1

sec

27°
(v)

1

√

sec

2

27°

−

1

Question 50

50.

Express
cot

34°
in terms of
cosec

34°

(i)

√

cosec

2

34°

−

1

(ii)

√

cosec

2

34°

−

1

cosec

34°

(iii)

1

cosec

34°

(iv)

cosec

34°

√

cosec

2

34°

−

1

(v)

1

√

cosec

2

34°

−

1

Question 51

51.

Express
sec

57°
in terms of
sin

57°

(i)

√

1

−

sin

2

57°

sin

57°

(ii)

√

1

−

sin

2

57°

(iii)

sin

57°

√

1

−

sin

2

57°

(iv)

1

sin

57°
(v)

1

√

1

−

sin

2

57°

Question 52

52.

Express
sec

43°
in terms of
cos

43°

(i)

cos

43°

√

1

−

cos

2

43°

(ii)

√

1

−

cos

2

43°

cos

43°

(iii)

1

√

1

−

cos

2

43°
(iv)

√

1

−

cos

2

43°
(v)

1

cos

43°

Question 53

53.

Express
sec

51°
in terms of
tan

51°

(i)

tan

51°

√

1

+

tan

2

51°

(ii)

√

1

+

tan

2

51°
(iii)

1

√

1

+

tan

2

51°
(iv)

1

tan

51°

(v)

√

1

+

tan

2

51°

tan

51°

Question 54

54.

Express
sec

25°
in terms of
cot

25°

(i)

1

cot

25°

(ii)

√

1

+

cot

2

25°

cot

25°

(iii)

√

1

+

cot

2

25°
(iv)

1

√

1

+

cot

2

25°

(v)

cot

25°

√

1

+

cot

2

25°

Question 55

55.

Express
sec

39°
in terms of
cosec

39°

(i)

√

cosec

2

39°

−

1

cosec

39°

(ii)

1

√

cosec

2

39°

−

1
(iii)

1

cosec

39°

(iv)

cosec

39°

√

cosec

2

39°

−

1

(v)

√

cosec

2

39°

−

1

Question 56

56.

Express
cosec

47°
in terms of
sin

47°

(i)

√

1

−

sin

2

47°

sin

47°

(ii)

1

√

1

−

sin

2

47°

(iii)

sin

47°

√

1

−

sin

2

47°

(iv)

√

1

−

sin

2

47°
(v)

1

sin

47°

Question 57

57.

Express
cosec

61°
in terms of
cos

61°

(i)

√

1

−

cos

2

61°

cos

61°

(ii)

1

cos

61°
(iii)

1

√

1

−

cos

2

61°
(iv)

√

1

−

cos

2

61°

(v)

cos

61°

√

1

−

cos

2

61°

Question 58

58.

Express
cosec

59°
in terms of
tan

59°

(i)

tan

59°

√

1

+

tan

2

59°

(ii)

1

√

1

+

tan

2

59°
(iii)

√

1

+

tan

2

59°

(iv)

√

1

+

tan

2

59°

tan

59°

(v)

1

tan

59°

Question 59

59.

Express
cosec

50°
in terms of
cot

50°

(i)

√

1

+

cot

2

50°

cot

50°

(ii)

√

1

+

cot

2

50°

(iii)

cot

50°

√

1

+

cot

2

50°

(iv)

1

cot

50°
(v)

1

√

1

+

cot

2

50°

Question 60

60.

Express
cosec

62°
in terms of
sec

62°

(i)

1

sec

62°

(ii)

sec

62°

√

sec

2

62°

−

1

(iii)

√

sec

2

62°

−

1

sec

62°

(iv)

1

√

sec

2

62°

−

1
(v)

√

sec

2

62°

−

1

Assignment Key