EduSahara™ Worksheet

EduSahara™ Assignment

Name : Trigonometric ratios in terms of other ratios

Chapter : Introduction to Trigonometry

Grade : CBSE Grade X

License : Non Commercial Use

Question 1

1.

Express
sin

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

1

cos

θ
(v)

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

Question 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

√

1

+

cot

2

θ
(iii)

1

√

1

+

cot

2

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

1

cot

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

1

sec

θ
(ii)

1

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

1

√

cosec

2

θ

−

1
(iii)

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

1

sin

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

√

1

−

sin

2

θ
(v)

1

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

tan

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

√

1

+

tan

2

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 8

8.

Express
cos

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 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

1

√

sec

2

θ

−

1
(iv)

1

sec

θ

(v)

sec

θ

√

sec

2

θ

−

1

Question 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

√

cosec

2

θ

−

1
(iii)

1

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

1

sin

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

√

1

−

sin

2

θ
(v)

1

√

1

−

sin

2

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

1

cos

θ
(ii)

√

1

−

cos

2

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

√

1

+

cot

2

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ
(v)

1

cot

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

sec

θ

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

1

√

sec

2

θ

−

1
(iv)

√

sec

2

θ

−

1
(v)

1

sec

θ

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

1

cosec

θ

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1
(v)

√

cosec

2

θ

−

1

Question 16

16.

Express
cot

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

sin

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ
(iv)

1

sin

θ
(v)

1

√

1

−

sin

2

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

cos

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

cos

θ
(iv)

1

√

1

−

cos

2

θ
(v)

√

1

−

cos

2

θ

Question 18

18.

Express
cot

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

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

sec

θ

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

1

√

sec

2

θ

−

1
(v)

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

cosec

θ

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ
(v)

√

cosec

2

θ

−

1

Question 21

21.

Express
sec

θ
in terms of
sin

θ

(i)

1

sin

θ
(ii)

√

1

−

sin

2

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

cos

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

cos

θ
(iv)

1

√

1

−

cos

2

θ
(v)

√

1

−

cos

2

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ
(ii)

√

1

+

tan

2

θ
(iii)

1

√

1

+

tan

2

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

tan

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

1

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ
(v)

1

√

1

+

cot

2

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

√

cosec

2

θ

−

1
(iii)

1

√

cosec

2

θ

−

1

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

1

cosec

θ

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

1

√

1

−

sin

2

θ
(ii)

√

1

−

sin

2

θ
(iii)

1

sin

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

sin

θ

√

1

−

sin

2

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

1

cos

θ
(ii)

1

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

Question 28

28.

Express
cosec

θ
in terms of
tan

θ

(i)

1

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

√

1

+

tan

2

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

tan

θ

Question 29

29.

Express
cosec

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ
(ii)

1

cot

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

sec

θ

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

1

sec

θ
(v)

1

√

sec

2

θ

−

1

Question 31

31.

Express
sin

74°
in terms of
cos

74°

(i)

1

√

1

−

cos

2

74°

(ii)

cos

74°

√

1

−

cos

2

74°

(iii)

√

1

−

cos

2

74°

cos

74°

(iv)

√

1

−

cos

2

74°
(v)

1

cos

74°

Question 32

32.

Express
sin

66°
in terms of
tan

66°

(i)

√

1

+

tan

2

66°
(ii)

1

tan

66°

(iii)

√

1

+

tan

2

66°

tan

66°

(iv)

tan

66°

√

1

+

tan

2

66°

(v)

1

√

1

+

tan

2

66°

Question 33

33.

Express
sin

70°
in terms of
cot

70°

(i)

√

1

+

cot

2

70°

cot

70°

(ii)

1

cot

70°
(iii)

√

1

+

cot

2

70°

(iv)

cot

70°

√

1

+

cot

2

70°

(v)

1

√

1

+

cot

2

70°

Question 34

34.

Express
sin

74°
in terms of
sec

74°

(i)

1

sec

74°
(ii)

√

sec

2

74°

−

1
(iii)

1

√

sec

2

74°

−

1

(iv)

√

sec

2

74°

−

1

sec

74°

(v)

sec

74°

√

sec

2

74°

−

1

Question 35

35.

Express
sin

65°
in terms of
cosec

65°

(i)

1

√

cosec

2

65°

−

1
(ii)

√

cosec

2

65°

−

1

(iii)

cosec

65°

√

cosec

2

65°

−

1

(iv)

√

cosec

2

65°

−

1

cosec

65°

(v)

1

cosec

65°

Question 36

36.

Express
cos

62°
in terms of
sin

62°

(i)

sin

62°

√

1

−

sin

2

62°

(ii)

√

1

−

sin

2

62°
(iii)

1

sin

62°

(iv)

√

1

−

sin

2

62°

sin

62°

(v)

1

√

1

−

sin

2

62°

Question 37

37.

Express
cos

22°
in terms of
tan

22°

(i)

1

√

1

+

tan

2

22°

(ii)

tan

22°

√

1

+

tan

2

22°

(iii)

1

tan

22°
(iv)

√

1

+

tan

2

22°

(v)

√

1

+

tan

2

22°

tan

22°

Question 38

38.

Express
cos

46°
in terms of
cot

46°

(i)

cot

46°

√

1

+

cot

2

46°

(ii)

√

1

+

cot

2

46°

cot

46°

(iii)

1

cot

46°
(iv)

√

1

+

cot

2

46°
(v)

1

√

1

+

cot

2

46°

Question 39

39.

Express
cos

34°
in terms of
sec

34°

(i)

√

sec

2

34°

−

1

sec

34°

(ii)

sec

34°

√

sec

2

34°

−

1

(iii)

1

sec

34°
(iv)

√

sec

2

34°

−

1
(v)

1

√

sec

2

34°

−

1

Question 40

40.

Express
cos

61°
in terms of
cosec

61°

(i)

√

cosec

2

61°

−

1

cosec

61°

(ii)

1

√

cosec

2

61°

−

1

(iii)

cosec

61°

√

cosec

2

61°

−

1

(iv)

√

cosec

2

61°

−

1
(v)

1

cosec

61°

Question 41

41.

Express
tan

49°
in terms of
sin

49°

(i)

sin

49°

√

1

−

sin

2

49°

(ii)

√

1

−

sin

2

49°

sin

49°

(iii)

√

1

−

sin

2

49°
(iv)

1

sin

49°
(v)

1

√

1

−

sin

2

49°

Question 42

42.

Express
tan

22°
in terms of
cos

22°

(i)

1

√

1

−

cos

2

22°
(ii)

√

1

−

cos

2

22°
(iii)

1

cos

22°

(iv)

√

1

−

cos

2

22°

cos

22°

(v)

cos

22°

√

1

−

cos

2

22°

Question 43

43.

Express
tan

48°
in terms of
cot

48°

(i)

1

cot

48°
(ii)

1

√

1

+

cot

2

48°

(iii)

√

1

+

cot

2

48°

cot

48°

(iv)

cot

48°

√

1

+

cot

2

48°

(v)

√

1

+

cot

2

48°

Question 44

44.

Express
tan

66°
in terms of
sec

66°

(i)

√

sec

2

66°

−

1
(ii)

1

√

sec

2

66°

−

1
(iii)

1

sec

66°

(iv)

√

sec

2

66°

−

1

sec

66°

(v)

sec

66°

√

sec

2

66°

−

1

Question 45

45.

Express
tan

23°
in terms of
cosec

23°

(i)

cosec

23°

√

cosec

2

23°

−

1

(ii)

√

cosec

2

23°

−

1

cosec

23°

(iii)

√

cosec

2

23°

−

1
(iv)

1

cosec

23°
(v)

1

√

cosec

2

23°

−

1

Question 46

46.

Express
cot

28°
in terms of
sin

28°

(i)

1

√

1

−

sin

2

28°
(ii)

1

sin

28°

(iii)

sin

28°

√

1

−

sin

2

28°

(iv)

√

1

−

sin

2

28°

sin

28°

(v)

√

1

−

sin

2

28°

Question 47

47.

Express
cot

55°
in terms of
cos

55°

(i)

1

cos

55°

(ii)

√

1

−

cos

2

55°

cos

55°

(iii)

√

1

−

cos

2

55°
(iv)

1

√

1

−

cos

2

55°

(v)

cos

55°

√

1

−

cos

2

55°

Question 48

48.

Express
cot

36°
in terms of
tan

36°

(i)

1

√

1

+

tan

2

36°
(ii)

√

1

+

tan

2

36°

(iii)

tan

36°

√

1

+

tan

2

36°

(iv)

√

1

+

tan

2

36°

tan

36°

(v)

1

tan

36°

Question 49

49.

Express
cot

26°
in terms of
sec

26°

(i)

sec

26°

√

sec

2

26°

−

1

(ii)

√

sec

2

26°

−

1

sec

26°

(iii)

1

sec

26°
(iv)

√

sec

2

26°

−

1
(v)

1

√

sec

2

26°

−

1

Question 50

50.

Express
cot

65°
in terms of
cosec

65°

(i)

cosec

65°

√

cosec

2

65°

−

1

(ii)

1

√

cosec

2

65°

−

1
(iii)

1

cosec

65°
(iv)

√

cosec

2

65°

−

1

(v)

√

cosec

2

65°

−

1

cosec

65°

Question 51

51.

Express
sec

57°
in terms of
sin

57°

(i)

√

1

−

sin

2

57°

(ii)

√

1

−

sin

2

57°

sin

57°

(iii)

1

sin

57°
(iv)

1

√

1

−

sin

2

57°

(v)

sin

57°

√

1

−

sin

2

57°

Question 52

52.

Express
sec

27°
in terms of
cos

27°

(i)

1

√

1

−

cos

2

27°

(ii)

cos

27°

√

1

−

cos

2

27°

(iii)

√

1

−

cos

2

27°

(iv)

√

1

−

cos

2

27°

cos

27°

(v)

1

cos

27°

Question 53

53.

Express
sec

40°
in terms of
tan

40°

(i)

tan

40°

√

1

+

tan

2

40°

(ii)

√

1

+

tan

2

40°
(iii)

1

tan

40°
(iv)

1

√

1

+

tan

2

40°

(v)

√

1

+

tan

2

40°

tan

40°

Question 54

54.

Express
sec

23°
in terms of
cot

23°

(i)

1

cot

23°
(ii)

√

1

+

cot

2

23°
(iii)

1

√

1

+

cot

2

23°

(iv)

cot

23°

√

1

+

cot

2

23°

(v)

√

1

+

cot

2

23°

cot

23°

Question 55

55.

Express
sec

53°
in terms of
cosec

53°

(i)

1

√

cosec

2

53°

−

1

(ii)

cosec

53°

√

cosec

2

53°

−

1

(iii)

√

cosec

2

53°

−

1

cosec

53°

(iv)

1

cosec

53°
(v)

√

cosec

2

53°

−

1

Question 56

56.

Express
cosec

75°
in terms of
sin

75°

(i)

1

sin

75°
(ii)

√

1

−

sin

2

75°

(iii)

sin

75°

√

1

−

sin

2

75°

(iv)

1

√

1

−

sin

2

75°

(v)

√

1

−

sin

2

75°

sin

75°

Question 57

57.

Express
cosec

28°
in terms of
cos

28°

(i)

1

cos

28°

(ii)

cos

28°

√

1

−

cos

2

28°

(iii)

√

1

−

cos

2

28°

(iv)

√

1

−

cos

2

28°

cos

28°

(v)

1

√

1

−

cos

2

28°

Question 58

58.

Express
cosec

49°
in terms of
tan

49°

(i)

√

1

+

tan

2

49°

tan

49°

(ii)

1

√

1

+

tan

2

49°
(iii)

√

1

+

tan

2

49°
(iv)

1

tan

49°

(v)

tan

49°

√

1

+

tan

2

49°

Question 59

59.

Express
cosec

27°
in terms of
cot

27°

(i)

√

1

+

cot

2

27°

cot

27°

(ii)

√

1

+

cot

2

27°
(iii)

1

√

1

+

cot

2

27°

(iv)

cot

27°

√

1

+

cot

2

27°

(v)

1

cot

27°

Question 60

60.

Express
cosec

36°
in terms of
sec

36°

(i)

√

sec

2

36°

−

1
(ii)

1

√

sec

2

36°

−

1
(iii)

1

sec

36°

(iv)

sec

36°

√

sec

2

36°

−

1

(v)

√

sec

2

36°

−

1

sec

36°

Assignment Key