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

−

cos

2

θ

cos

θ

(ii)

√

1

−

cos

2

θ
(iii)

1

cos

θ
(iv)

1

√

1

−

cos

2

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

1

tan

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

√

1

+

tan

2

θ
(v)

1

√

1

+

tan

2

θ

Question 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ
(iv)

1

cot

θ
(v)

1

√

1

+

cot

2

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

sec

θ

√

sec

2

θ

−

1

(ii)

1

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1
(v)

1

sec

θ

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

cosec

θ
(ii)

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

1

√

1

−

sin

2

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

1

sin

θ
(v)

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

1

tan

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

√

1

+

tan

2

θ
(iv)

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

tan

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

1

cot

θ
(iii)

√

1

+

cot

2

θ
(iv)

1

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

√

sec

2

θ

−

1
(iii)

1

sec

θ

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

1

√

sec

2

θ

−

1

Question 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

cosec

θ

(iii)

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ
(ii)

1

√

1

−

sin

2

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

1

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

√

1

−

cos

2

θ
(v)

1

cos

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

(ii)

√

1

+

cot

2

θ

cot

θ

(iii)

1

√

1

+

cot

2

θ
(iv)

1

cot

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 14

14.

Express
tan

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

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

cosec

θ

(iii)

1

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 16

16.

Express
cot

θ
in terms of
sin

θ

(i)

1

√

1

−

sin

2

θ
(ii)

√

1

−

sin

2

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

1

cos

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)

1

tan

θ
(iv)

√

1

+

tan

2

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 19

19.

Express
cot

θ
in terms of
sec

θ

(i)

sec

θ

√

sec

2

θ

−

1

(ii)

1

√

sec

2

θ

−

1
(iii)

1

sec

θ
(iv)

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

sec

θ

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1
(ii)

1

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

cosec

θ

(v)

cosec

θ

√

cosec

2

θ

−

1

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

2

θ

sin

θ

(iv)

1

sin

θ

(v)

sin

θ

√

1

−

sin

2

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)

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

√

1

+

tan

2

θ
(iv)

1

tan

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

1

cot

θ
(iii)

√

1

+

cot

2

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

1

√

1

+

cot

2

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

1

cosec

θ
(ii)

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

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

2

θ
(v)

1

sin

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

cos

θ

(ii)

1

cos

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

√

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)

tan

θ

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

√

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)

cot

θ

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

1

cot

θ
(v)

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

1

sec

θ
(iv)

1

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

sec

θ

Question 31

31.

Express
sin

65°
in terms of
cos

65°

(i)

1

cos

65°
(ii)

√

1

−

cos

2

65°

(iii)

cos

65°

√

1

−

cos

2

65°

(iv)

1

√

1

−

cos

2

65°

(v)

√

1

−

cos

2

65°

cos

65°

Question 32

32.

Express
sin

55°
in terms of
tan

55°

(i)

1

tan

55°

(ii)

tan

55°

√

1

+

tan

2

55°

(iii)

√

1

+

tan

2

55°

(iv)

√

1

+

tan

2

55°

tan

55°

(v)

1

√

1

+

tan

2

55°

Question 33

33.

Express
sin

63°
in terms of
cot

63°

(i)

√

1

+

cot

2

63°
(ii)

1

cot

63°

(iii)

cot

63°

√

1

+

cot

2

63°

(iv)

√

1

+

cot

2

63°

cot

63°

(v)

1

√

1

+

cot

2

63°

Question 34

34.

Express
sin

38°
in terms of
sec

38°

(i)

√

sec

2

38°

−

1

(ii)

√

sec

2

38°

−

1

sec

38°

(iii)

1

√

sec

2

38°

−

1
(iv)

1

sec

38°

(v)

sec

38°

√

sec

2

38°

−

1

Question 35

35.

Express
sin

22°
in terms of
cosec

22°

(i)

√

cosec

2

22°

−

1

cosec

22°

(ii)

1

cosec

22°
(iii)

√

cosec

2

22°

−

1
(iv)

1

√

cosec

2

22°

−

1

(v)

cosec

22°

√

cosec

2

22°

−

1

Question 36

36.

Express
cos

71°
in terms of
sin

71°

(i)

1

sin

71°
(ii)

1

√

1

−

sin

2

71°

(iii)

√

1

−

sin

2

71°

sin

71°

(iv)

√

1

−

sin

2

71°

(v)

sin

71°

√

1

−

sin

2

71°

Question 37

37.

Express
cos

27°
in terms of
tan

27°

(i)

tan

27°

√

1

+

tan

2

27°

(ii)

1

tan

27°
(iii)

√

1

+

tan

2

27°

(iv)

√

1

+

tan

2

27°

tan

27°

(v)

1

√

1

+

tan

2

27°

Question 38

38.

Express
cos

55°
in terms of
cot

55°

(i)

1

√

1

+

cot

2

55°

(ii)

cot

55°

√

1

+

cot

2

55°

(iii)

1

cot

55°

(iv)

√

1

+

cot

2

55°

cot

55°

(v)

√

1

+

cot

2

55°

Question 39

39.

Express
cos

55°
in terms of
sec

55°

(i)

√

sec

2

55°

−

1

sec

55°

(ii)

1

sec

55°
(iii)

1

√

sec

2

55°

−

1
(iv)

√

sec

2

55°

−

1

(v)

sec

55°

√

sec

2

55°

−

1

Question 40

40.

Express
cos

72°
in terms of
cosec

72°

(i)

√

cosec

2

72°

−

1

cosec

72°

(ii)

1

cosec

72°
(iii)

√

cosec

2

72°

−

1

(iv)

cosec

72°

√

cosec

2

72°

−

1

(v)

1

√

cosec

2

72°

−

1

Question 41

41.

Express
tan

27°
in terms of
sin

27°

(i)

1

√

1

−

sin

2

27°

(ii)

√

1

−

sin

2

27°

sin

27°

(iii)

sin

27°

√

1

−

sin

2

27°

(iv)

1

sin

27°
(v)

√

1

−

sin

2

27°

Question 42

42.

Express
tan

62°
in terms of
cos

62°

(i)

√

1

−

cos

2

62°

cos

62°

(ii)

1

cos

62°

(iii)

cos

62°

√

1

−

cos

2

62°

(iv)

√

1

−

cos

2

62°
(v)

1

√

1

−

cos

2

62°

Question 43

43.

Express
tan

27°
in terms of
cot

27°

(i)

cot

27°

√

1

+

cot

2

27°

(ii)

√

1

+

cot

2

27°

cot

27°

(iii)

1

cot

27°
(iv)

1

√

1

+

cot

2

27°
(v)

√

1

+

cot

2

27°

Question 44

44.

Express
tan

72°
in terms of
sec

72°

(i)

√

sec

2

72°

−

1

(ii)

√

sec

2

72°

−

1

sec

72°

(iii)

1

sec

72°
(iv)

1

√

sec

2

72°

−

1

(v)

sec

72°

√

sec

2

72°

−

1

Question 45

45.

Express
tan

58°
in terms of
cosec

58°

(i)

cosec

58°

√

cosec

2

58°

−

1

(ii)

1

√

cosec

2

58°

−

1

(iii)

√

cosec

2

58°

−

1

cosec

58°

(iv)

√

cosec

2

58°

−

1
(v)

1

cosec

58°

Question 46

46.

Express
cot

24°
in terms of
sin

24°

(i)

1

√

1

−

sin

2

24°

(ii)

√

1

−

sin

2

24°

sin

24°

(iii)

sin

24°

√

1

−

sin

2

24°

(iv)

1

sin

24°
(v)

√

1

−

sin

2

24°

Question 47

47.

Express
cot

60°
in terms of
cos

60°

(i)

√

1

−

cos

2

60°

cos

60°

(ii)

1

cos

60°
(iii)

√

1

−

cos

2

60°
(iv)

1

√

1

−

cos

2

60°

(v)

cos

60°

√

1

−

cos

2

60°

Question 48

48.

Express
cot

49°
in terms of
tan

49°

(i)

1

√

1

+

tan

2

49°

(ii)

√

1

+

tan

2

49°

tan

49°

(iii)

1

tan

49°

(iv)

tan

49°

√

1

+

tan

2

49°

(v)

√

1

+

tan

2

49°

Question 49

49.

Express
cot

45°
in terms of
sec

45°

(i)

sec

45°

√

sec

2

45°

−

1

(ii)

√

sec

2

45°

−

1
(iii)

1

√

sec

2

45°

−

1
(iv)

1

sec

45°

(v)

√

sec

2

45°

−

1

sec

45°

Question 50

50.

Express
cot

65°
in terms of
cosec

65°

(i)

1

cosec

65°
(ii)

√

cosec

2

65°

−

1

(iii)

√

cosec

2

65°

−

1

cosec

65°

(iv)

cosec

65°

√

cosec

2

65°

−

1

(v)

1

√

cosec

2

65°

−

1

Question 51

51.

Express
sec

20°
in terms of
sin

20°

(i)

1

sin

20°

(ii)

√

1

−

sin

2

20°

sin

20°

(iii)

sin

20°

√

1

−

sin

2

20°

(iv)

1

√

1

−

sin

2

20°
(v)

√

1

−

sin

2

20°

Question 52

52.

Express
sec

21°
in terms of
cos

21°

(i)

√

1

−

cos

2

21°

(ii)

cos

21°

√

1

−

cos

2

21°

(iii)

1

cos

21°
(iv)

1

√

1

−

cos

2

21°

(v)

√

1

−

cos

2

21°

cos

21°

Question 53

53.

Express
sec

56°
in terms of
tan

56°

(i)

1

tan

56°
(ii)

1

√

1

+

tan

2

56°

(iii)

√

1

+

tan

2

56°

tan

56°

(iv)

tan

56°

√

1

+

tan

2

56°

(v)

√

1

+

tan

2

56°

Question 54

54.

Express
sec

38°
in terms of
cot

38°

(i)

√

1

+

cot

2

38°

(ii)

cot

38°

√

1

+

cot

2

38°

(iii)

√

1

+

cot

2

38°

cot

38°

(iv)

1

cot

38°
(v)

1

√

1

+

cot

2

38°

Question 55

55.

Express
sec

44°
in terms of
cosec

44°

(i)

√

cosec

2

44°

−

1

cosec

44°

(ii)

1

cosec

44°

(iii)

cosec

44°

√

cosec

2

44°

−

1

(iv)

1

√

cosec

2

44°

−

1
(v)

√

cosec

2

44°

−

1

Question 56

56.

Express
cosec

27°
in terms of
sin

27°

(i)

sin

27°

√

1

−

sin

2

27°

(ii)

1

sin

27°

(iii)

√

1

−

sin

2

27°

sin

27°

(iv)

1

√

1

−

sin

2

27°
(v)

√

1

−

sin

2

27°

Question 57

57.

Express
cosec

76°
in terms of
cos

76°

(i)

1

cos

76°
(ii)

1

√

1

−

cos

2

76°

(iii)

cos

76°

√

1

−

cos

2

76°

(iv)

√

1

−

cos

2

76°

(v)

√

1

−

cos

2

76°

cos

76°

Question 58

58.

Express
cosec

31°
in terms of
tan

31°

(i)

1

√

1

+

tan

2

31°

(ii)

tan

31°

√

1

+

tan

2

31°

(iii)

1

tan

31°

(iv)

√

1

+

tan

2

31°

tan

31°

(v)

√

1

+

tan

2

31°

Question 59

59.

Express
cosec

62°
in terms of
cot

62°

(i)

cot

62°

√

1

+

cot

2

62°

(ii)

√

1

+

cot

2

62°
(iii)

1

√

1

+

cot

2

62°
(iv)

1

cot

62°

(v)

√

1

+

cot

2

62°

cot

62°

Question 60

60.

Express
cosec

47°
in terms of
sec

47°

(i)

√

sec

2

47°

−

1

sec

47°

(ii)

√

sec

2

47°

−

1
(iii)

1

√

sec

2

47°

−

1

(iv)

sec

47°

√

sec

2

47°

−

1

(v)

1

sec

47°

Assignment Key