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

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

1

√

1

−

cos

2

θ
(iv)

√

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)

1

√

1

+

tan

2

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

√

1

+

tan

2

θ

Question 3

3.

Express
sin

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 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

1

sec

θ
(iv)

1

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1
(ii)

√

cosec

2

θ

−

1
(iii)

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

1

√

1

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

1

sin

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

1

tan

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ
(ii)

1

√

1

+

cot

2

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

1

cot

θ
(v)

√

1

+

cot

2

θ

cot

θ

Question 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

1

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1
(v)

1

sec

θ

Question 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1
(ii)

1

cosec

θ

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

√

cosec

2

θ

−

1

cosec

θ

(v)

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ
(v)

1

√

1

−

sin

2

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

cos

θ
(v)

1

√

1

−

cos

2

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

√

1

+

cot

2

θ
(iii)

1

√

1

+

cot

2

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

√

1

+

cot

2

θ

cot

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

1

sec

θ
(v)

1

√

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)

1

√

1

−

sin

2

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

1

sin

θ
(iv)

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 17

17.

Express
cot

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 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

√

1

+

tan

2

θ
(iv)

√

1

+

tan

2

θ
(v)

1

tan

θ

Question 19

19.

Express
cot

θ
in terms of
sec

θ

(i)

1

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1
(v)

1

sec

θ

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

√

cosec

2

θ

−

1
(iii)

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

1

√

cosec

2

θ

−

1

Question 21

21.

Express
sec

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

√

1

−

sin

2

θ
(v)

√

1

−

sin

2

θ

Question 22

22.

Express
sec

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

2

θ
(v)

1

cos

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

1

tan

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

√

1

+

tan

2

θ

tan

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ
(ii)

1

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

cot

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

1

√

cosec

2

θ

−

1
(iii)

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

1

sin

θ
(iv)

1

√

1

−

sin

2

θ
(v)

√

1

−

sin

2

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

1

√

1

−

cos

2

θ
(iii)

1

cos

θ
(iv)

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

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

tan

θ

(iii)

√

1

+

tan

2

θ
(iv)

1

tan

θ
(v)

1

√

1

+

tan

2

θ

Question 29

29.

Express
cosec

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 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

1

sec

θ

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

√

sec

2

θ

−

1

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

1

√

sec

2

θ

−

1

Question 31

31.

Express
sin

29°
in terms of
cos

29°

(i)

cos

29°

√

1

−

cos

2

29°

(ii)

1

cos

29°

(iii)

√

1

−

cos

2

29°

cos

29°

(iv)

√

1

−

cos

2

29°
(v)

1

√

1

−

cos

2

29°

Question 32

32.

Express
sin

60°
in terms of
tan

60°

(i)

√

1

+

tan

2

60°

tan

60°

(ii)

tan

60°

√

1

+

tan

2

60°

(iii)

√

1

+

tan

2

60°
(iv)

1

√

1

+

tan

2

60°
(v)

1

tan

60°

Question 33

33.

Express
sin

51°
in terms of
cot

51°

(i)

1

√

1

+

cot

2

51°
(ii)

1

cot

51°
(iii)

√

1

+

cot

2

51°

(iv)

√

1

+

cot

2

51°

cot

51°

(v)

cot

51°

√

1

+

cot

2

51°

Question 34

34.

Express
sin

50°
in terms of
sec

50°

(i)

1

√

sec

2

50°

−

1

(ii)

√

sec

2

50°

−

1

sec

50°

(iii)

sec

50°

√

sec

2

50°

−

1

(iv)

1

sec

50°
(v)

√

sec

2

50°

−

1

Question 35

35.

Express
sin

70°
in terms of
cosec

70°

(i)

1

√

cosec

2

70°

−

1

(ii)

√

cosec

2

70°

−

1

cosec

70°

(iii)

cosec

70°

√

cosec

2

70°

−

1

(iv)

√

cosec

2

70°

−

1
(v)

1

cosec

70°

Question 36

36.

Express
cos

40°
in terms of
sin

40°

(i)

1

sin

40°

(ii)

sin

40°

√

1

−

sin

2

40°

(iii)

√

1

−

sin

2

40°
(iv)

1

√

1

−

sin

2

40°

(v)

√

1

−

sin

2

40°

sin

40°

Question 37

37.

Express
cos

32°
in terms of
tan

32°

(i)

tan

32°

√

1

+

tan

2

32°

(ii)

1

√

1

+

tan

2

32°

(iii)

√

1

+

tan

2

32°

tan

32°

(iv)

1

tan

32°
(v)

√

1

+

tan

2

32°

Question 38

38.

Express
cos

29°
in terms of
cot

29°

(i)

√

1

+

cot

2

29°

cot

29°

(ii)

1

cot

29°
(iii)

√

1

+

cot

2

29°

(iv)

cot

29°

√

1

+

cot

2

29°

(v)

1

√

1

+

cot

2

29°

Question 39

39.

Express
cos

61°
in terms of
sec

61°

(i)

1

sec

61°

(ii)

√

sec

2

61°

−

1

sec

61°

(iii)

1

√

sec

2

61°

−

1
(iv)

√

sec

2

61°

−

1

(v)

sec

61°

√

sec

2

61°

−

1

Question 40

40.

Express
cos

49°
in terms of
cosec

49°

(i)

√

cosec

2

49°

−

1

cosec

49°

(ii)

1

√

cosec

2

49°

−

1
(iii)

1

cosec

49°
(iv)

√

cosec

2

49°

−

1

(v)

cosec

49°

√

cosec

2

49°

−

1

Question 41

41.

Express
tan

70°
in terms of
sin

70°

(i)

1

sin

70°
(ii)

√

1

−

sin

2

70°
(iii)

1

√

1

−

sin

2

70°

(iv)

sin

70°

√

1

−

sin

2

70°

(v)

√

1

−

sin

2

70°

sin

70°

Question 42

42.

Express
tan

35°
in terms of
cos

35°

(i)

1

cos

35°
(ii)

1

√

1

−

cos

2

35°

(iii)

√

1

−

cos

2

35°

cos

35°

(iv)

cos

35°

√

1

−

cos

2

35°

(v)

√

1

−

cos

2

35°

Question 43

43.

Express
tan

55°
in terms of
cot

55°

(i)

cot

55°

√

1

+

cot

2

55°

(ii)

1

cot

55°
(iii)

√

1

+

cot

2

55°

(iv)

√

1

+

cot

2

55°

cot

55°

(v)

1

√

1

+

cot

2

55°

Question 44

44.

Express
tan

39°
in terms of
sec

39°

(i)

√

sec

2

39°

−

1

sec

39°

(ii)

sec

39°

√

sec

2

39°

−

1

(iii)

√

sec

2

39°

−

1
(iv)

1

√

sec

2

39°

−

1
(v)

1

sec

39°

Question 45

45.

Express
tan

33°
in terms of
cosec

33°

(i)

√

cosec

2

33°

−

1

(ii)

cosec

33°

√

cosec

2

33°

−

1

(iii)

1

√

cosec

2

33°

−

1
(iv)

1

cosec

33°

(v)

√

cosec

2

33°

−

1

cosec

33°

Question 46

46.

Express
cot

50°
in terms of
sin

50°

(i)

√

1

−

sin

2

50°
(ii)

1

√

1

−

sin

2

50°

(iii)

√

1

−

sin

2

50°

sin

50°

(iv)

sin

50°

√

1

−

sin

2

50°

(v)

1

sin

50°

Question 47

47.

Express
cot

63°
in terms of
cos

63°

(i)

√

1

−

cos

2

63°

(ii)

cos

63°

√

1

−

cos

2

63°

(iii)

√

1

−

cos

2

63°

cos

63°

(iv)

1

√

1

−

cos

2

63°
(v)

1

cos

63°

Question 48

48.

Express
cot

47°
in terms of
tan

47°

(i)

1

tan

47°
(ii)

√

1

+

tan

2

47°
(iii)

1

√

1

+

tan

2

47°

(iv)

√

1

+

tan

2

47°

tan

47°

(v)

tan

47°

√

1

+

tan

2

47°

Question 49

49.

Express
cot

23°
in terms of
sec

23°

(i)

√

sec

2

23°

−

1

(ii)

sec

23°

√

sec

2

23°

−

1

(iii)

1

√

sec

2

23°

−

1

(iv)

√

sec

2

23°

−

1

sec

23°

(v)

1

sec

23°

Question 50

50.

Express
cot

29°
in terms of
cosec

29°

(i)

√

cosec

2

29°

−

1

(ii)

cosec

29°

√

cosec

2

29°

−

1

(iii)

√

cosec

2

29°

−

1

cosec

29°

(iv)

1

√

cosec

2

29°

−

1
(v)

1

cosec

29°

Question 51

51.

Express
sec

67°
in terms of
sin

67°

(i)

√

1

−

sin

2

67°

sin

67°

(ii)

1

sin

67°
(iii)

√

1

−

sin

2

67°
(iv)

1

√

1

−

sin

2

67°

(v)

sin

67°

√

1

−

sin

2

67°

Question 52

52.

Express
sec

74°
in terms of
cos

74°

(i)

√

1

−

cos

2

74°

(ii)

√

1

−

cos

2

74°

cos

74°

(iii)

1

cos

74°
(iv)

1

√

1

−

cos

2

74°

(v)

cos

74°

√

1

−

cos

2

74°

Question 53

53.

Express
sec

76°
in terms of
tan

76°

(i)

tan

76°

√

1

+

tan

2

76°

(ii)

1

tan

76°
(iii)

1

√

1

+

tan

2

76°

(iv)

√

1

+

tan

2

76°

tan

76°

(v)

√

1

+

tan

2

76°

Question 54

54.

Express
sec

51°
in terms of
cot

51°

(i)

cot

51°

√

1

+

cot

2

51°

(ii)

√

1

+

cot

2

51°
(iii)

1

√

1

+

cot

2

51°

(iv)

√

1

+

cot

2

51°

cot

51°

(v)

1

cot

51°

Question 55

55.

Express
sec

60°
in terms of
cosec

60°

(i)

1

√

cosec

2

60°

−

1
(ii)

1

cosec

60°

(iii)

cosec

60°

√

cosec

2

60°

−

1

(iv)

√

cosec

2

60°

−

1

(v)

√

cosec

2

60°

−

1

cosec

60°

Question 56

56.

Express
cosec

52°
in terms of
sin

52°

(i)

1

√

1

−

sin

2

52°

(ii)

sin

52°

√

1

−

sin

2

52°

(iii)

√

1

−

sin

2

52°

sin

52°

(iv)

1

sin

52°
(v)

√

1

−

sin

2

52°

Question 57

57.

Express
cosec

41°
in terms of
cos

41°

(i)

1

cos

41°

(ii)

√

1

−

cos

2

41°

cos

41°

(iii)

cos

41°

√

1

−

cos

2

41°

(iv)

1

√

1

−

cos

2

41°
(v)

√

1

−

cos

2

41°

Question 58

58.

Express
cosec

29°
in terms of
tan

29°

(i)

tan

29°

√

1

+

tan

2

29°

(ii)

√

1

+

tan

2

29°
(iii)

1

tan

29°
(iv)

1

√

1

+

tan

2

29°

(v)

√

1

+

tan

2

29°

tan

29°

Question 59

59.

Express
cosec

35°
in terms of
cot

35°

(i)

√

1

+

cot

2

35°

cot

35°

(ii)

1

cot

35°
(iii)

1

√

1

+

cot

2

35°
(iv)

√

1

+

cot

2

35°

(v)

cot

35°

√

1

+

cot

2

35°

Question 60

60.

Express
cosec

68°
in terms of
sec

68°

(i)

√

sec

2

68°

−

1

sec

68°

(ii)

1

√

sec

2

68°

−

1
(iii)

√

sec

2

68°

−

1
(iv)

1

sec

68°

(v)

sec

68°

√

sec

2

68°

−

1

Assignment Key