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

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ
(v)

1

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

1

√

1

+

tan

2

θ
(ii)

√

1

+

tan

2

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

1

tan

θ

Question 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ
(ii)

1

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

cot

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)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

1

√

sec

2

θ

−

1
(v)

√

sec

2

θ

−

1

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)

cosec

θ

√

cosec

2

θ

−

1

(v)

1

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

1

√

1

−

sin

2

θ
(iii)

√

1

−

sin

2

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

1

sin

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

tan

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

1

√

1

+

tan

2

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

1

cot

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

1

√

1

+

cot

2

θ
(iv)

√

1

+

cot

2

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)

1

sec

θ

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1
(ii)

1

cosec

θ
(iii)

1

√

cosec

2

θ

−

1

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

sin

θ

(ii)

1

sin

θ
(iii)

1

√

1

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

√

1

−

cos

2

θ
(iv)

1

√

1

−

cos

2

θ
(v)

1

cos

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)

1

cot

θ
(iv)

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

1

sec

θ

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1
(iv)

1

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

sec

θ

Question 15

15.

Express
tan

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 16

16.

Express
cot

θ
in terms of
sin

θ

(i)

1

sin

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

1

√

1

−

sin

2

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ
(ii)

1

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

1

cos

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

2

θ

−

1
(ii)

√

sec

2

θ

−

1
(iii)

1

sec

θ

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

sec

θ

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

cosec

θ
(v)

√

cosec

2

θ

−

1

Question 21

21.

Express
sec

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

1

√

1

−

sin

2

θ
(iv)

√

1

−

sin

2

θ
(v)

1

sin

θ

Question 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

1

cos

θ
(ii)

1

√

1

−

cos

2

θ
(iii)

√

1

−

cos

2

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

cos

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

tan

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

1

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ
(ii)

1

√

1

+

cot

2

θ
(iii)

1

cot

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

√

1

+

cot

2

θ

cot

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

1

√

cosec

2

θ

−

1
(iii)

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

sin

θ

(ii)

√

1

−

sin

2

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

√

1

−

sin

2

θ
(v)

1

sin

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

1

√

1

−

cos

2

θ
(v)

1

cos

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
(iv)

1

tan

θ
(v)

√

1

+

tan

2

θ

tan

θ

Question 29

29.

Express
cosec

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

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

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

sec

θ

(v)

√

sec

2

θ

−

1

Question 31

31.

Express
sin

23°
in terms of
cos

23°

(i)

√

1

−

cos

2

23°

cos

23°

(ii)

√

1

−

cos

2

23°

(iii)

cos

23°

√

1

−

cos

2

23°

(iv)

1

cos

23°
(v)

1

√

1

−

cos

2

23°

Question 32

32.

Express
sin

65°
in terms of
tan

65°

(i)

1

tan

65°
(ii)

1

√

1

+

tan

2

65°

(iii)

tan

65°

√

1

+

tan

2

65°

(iv)

√

1

+

tan

2

65°

tan

65°

(v)

√

1

+

tan

2

65°

Question 33

33.

Express
sin

60°
in terms of
cot

60°

(i)

1

cot

60°
(ii)

1

√

1

+

cot

2

60°
(iii)

√

1

+

cot

2

60°

(iv)

√

1

+

cot

2

60°

cot

60°

(v)

cot

60°

√

1

+

cot

2

60°

Question 34

34.

Express
sin

54°
in terms of
sec

54°

(i)

√

sec

2

54°

−

1

sec

54°

(ii)

sec

54°

√

sec

2

54°

−

1

(iii)

√

sec

2

54°

−

1
(iv)

1

sec

54°
(v)

1

√

sec

2

54°

−

1

Question 35

35.

Express
sin

24°
in terms of
cosec

24°

(i)

√

cosec

2

24°

−

1

(ii)

√

cosec

2

24°

−

1

cosec

24°

(iii)

cosec

24°

√

cosec

2

24°

−

1

(iv)

1

cosec

24°
(v)

1

√

cosec

2

24°

−

1

Question 36

36.

Express
cos

51°
in terms of
sin

51°

(i)

sin

51°

√

1

−

sin

2

51°

(ii)

√

1

−

sin

2

51°
(iii)

1

sin

51°
(iv)

1

√

1

−

sin

2

51°

(v)

√

1

−

sin

2

51°

sin

51°

Question 37

37.

Express
cos

22°
in terms of
tan

22°

(i)

√

1

+

tan

2

22°

tan

22°

(ii)

1

√

1

+

tan

2

22°

(iii)

tan

22°

√

1

+

tan

2

22°

(iv)

1

tan

22°
(v)

√

1

+

tan

2

22°

Question 38

38.

Express
cos

38°
in terms of
cot

38°

(i)

√

1

+

cot

2

38°

cot

38°

(ii)

1

cot

38°
(iii)

√

1

+

cot

2

38°
(iv)

1

√

1

+

cot

2

38°

(v)

cot

38°

√

1

+

cot

2

38°

Question 39

39.

Express
cos

27°
in terms of
sec

27°

(i)

1

sec

27°

(ii)

sec

27°

√

sec

2

27°

−

1

(iii)

1

√

sec

2

27°

−

1

(iv)

√

sec

2

27°

−

1

sec

27°

(v)

√

sec

2

27°

−

1

Question 40

40.

Express
cos

55°
in terms of
cosec

55°

(i)

cosec

55°

√

cosec

2

55°

−

1

(ii)

1

√

cosec

2

55°

−

1

(iii)

√

cosec

2

55°

−

1

cosec

55°

(iv)

1

cosec

55°
(v)

√

cosec

2

55°

−

1

Question 41

41.

Express
tan

50°
in terms of
sin

50°

(i)

1

√

1

−

sin

2

50°
(ii)

√

1

−

sin

2

50°

(iii)

√

1

−

sin

2

50°

sin

50°

(iv)

1

sin

50°

(v)

sin

50°

√

1

−

sin

2

50°

Question 42

42.

Express
tan

49°
in terms of
cos

49°

(i)

√

1

−

cos

2

49°
(ii)

1

cos

49°

(iii)

√

1

−

cos

2

49°

cos

49°

(iv)

cos

49°

√

1

−

cos

2

49°

(v)

1

√

1

−

cos

2

49°

Question 43

43.

Express
tan

40°
in terms of
cot

40°

(i)

1

√

1

+

cot

2

40°

(ii)

cot

40°

√

1

+

cot

2

40°

(iii)

1

cot

40°
(iv)

√

1

+

cot

2

40°

(v)

√

1

+

cot

2

40°

cot

40°

Question 44

44.

Express
tan

55°
in terms of
sec

55°

(i)

√

sec

2

55°

−

1

(ii)

sec

55°

√

sec

2

55°

−

1

(iii)

1

sec

55°

(iv)

√

sec

2

55°

−

1

sec

55°

(v)

1

√

sec

2

55°

−

1

Question 45

45.

Express
tan

34°
in terms of
cosec

34°

(i)

√

cosec

2

34°

−

1

cosec

34°

(ii)

cosec

34°

√

cosec

2

34°

−

1

(iii)

√

cosec

2

34°

−

1
(iv)

1

cosec

34°
(v)

1

√

cosec

2

34°

−

1

Question 46

46.

Express
cot

59°
in terms of
sin

59°

(i)

√

1

−

sin

2

59°

sin

59°

(ii)

1

√

1

−

sin

2

59°
(iii)

√

1

−

sin

2

59°

(iv)

sin

59°

√

1

−

sin

2

59°

(v)

1

sin

59°

Question 47

47.

Express
cot

77°
in terms of
cos

77°

(i)

√

1

−

cos

2

77°

(ii)

cos

77°

√

1

−

cos

2

77°

(iii)

1

√

1

−

cos

2

77°

(iv)

√

1

−

cos

2

77°

cos

77°

(v)

1

cos

77°

Question 48

48.

Express
cot

54°
in terms of
tan

54°

(i)

tan

54°

√

1

+

tan

2

54°

(ii)

1

tan

54°

(iii)

√

1

+

tan

2

54°

tan

54°

(iv)

√

1

+

tan

2

54°
(v)

1

√

1

+

tan

2

54°

Question 49

49.

Express
cot

41°
in terms of
sec

41°

(i)

√

sec

2

41°

−

1

sec

41°

(ii)

1

√

sec

2

41°

−

1
(iii)

√

sec

2

41°

−

1

(iv)

sec

41°

√

sec

2

41°

−

1

(v)

1

sec

41°

Question 50

50.

Express
cot

62°
in terms of
cosec

62°

(i)

√

cosec

2

62°

−

1

(ii)

cosec

62°

√

cosec

2

62°

−

1

(iii)

1

√

cosec

2

62°

−

1

(iv)

√

cosec

2

62°

−

1

cosec

62°

(v)

1

cosec

62°

Question 51

51.

Express
sec

22°
in terms of
sin

22°

(i)

√

1

−

sin

2

22°

sin

22°

(ii)

√

1

−

sin

2

22°
(iii)

1

√

1

−

sin

2

22°

(iv)

sin

22°

√

1

−

sin

2

22°

(v)

1

sin

22°

Question 52

52.

Express
sec

60°
in terms of
cos

60°

(i)

√

1

−

cos

2

60°

cos

60°

(ii)

1

√

1

−

cos

2

60°
(iii)

1

cos

60°
(iv)

√

1

−

cos

2

60°

(v)

cos

60°

√

1

−

cos

2

60°

Question 53

53.

Express
sec

78°
in terms of
tan

78°

(i)

1

√

1

+

tan

2

78°
(ii)

√

1

+

tan

2

78°

(iii)

tan

78°

√

1

+

tan

2

78°

(iv)

1

tan

78°

(v)

√

1

+

tan

2

78°

tan

78°

Question 54

54.

Express
sec

54°
in terms of
cot

54°

(i)

√

1

+

cot

2

54°
(ii)

1

√

1

+

cot

2

54°

(iii)

√

1

+

cot

2

54°

cot

54°

(iv)

1

cot

54°

(v)

cot

54°

√

1

+

cot

2

54°

Question 55

55.

Express
sec

25°
in terms of
cosec

25°

(i)

√

cosec

2

25°

−

1

cosec

25°

(ii)

cosec

25°

√

cosec

2

25°

−

1

(iii)

1

√

cosec

2

25°

−

1
(iv)

1

cosec

25°
(v)

√

cosec

2

25°

−

1

Question 56

56.

Express
cosec

29°
in terms of
sin

29°

(i)

√

1

−

sin

2

29°

sin

29°

(ii)

1

√

1

−

sin

2

29°

(iii)

sin

29°

√

1

−

sin

2

29°

(iv)

1

sin

29°
(v)

√

1

−

sin

2

29°

Question 57

57.

Express
cosec

40°
in terms of
cos

40°

(i)

cos

40°

√

1

−

cos

2

40°

(ii)

1

cos

40°
(iii)

1

√

1

−

cos

2

40°
(iv)

√

1

−

cos

2

40°

(v)

√

1

−

cos

2

40°

cos

40°

Question 58

58.

Express
cosec

50°
in terms of
tan

50°

(i)

1

tan

50°

(ii)

√

1

+

tan

2

50°

tan

50°

(iii)

tan

50°

√

1

+

tan

2

50°

(iv)

1

√

1

+

tan

2

50°
(v)

√

1

+

tan

2

50°

Question 59

59.

Express
cosec

60°
in terms of
cot

60°

(i)

1

√

1

+

cot

2

60°

(ii)

√

1

+

cot

2

60°

cot

60°

(iii)

√

1

+

cot

2

60°

(iv)

cot

60°

√

1

+

cot

2

60°

(v)

1

cot

60°

Question 60

60.

Express
cosec

80°
in terms of
sec

80°

(i)

sec

80°

√

sec

2

80°

−

1

(ii)

1

sec

80°

(iii)

√

sec

2

80°

−

1

sec

80°

(iv)

1

√

sec

2

80°

−

1
(v)

√

sec

2

80°

−

1

Assignment Key