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)

cos

θ

√

1

−

cos

2

θ

(ii)

1

cos

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

√

1

−

cos

2

θ
(v)

1

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

√

1

+

tan

2

θ
(iv)

1

tan

θ
(v)

√

1

+

tan

2

θ

tan

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)

cot

θ

√

1

+

cot

2

θ

(iv)

1

√

1

+

cot

2

θ
(v)

1

cot

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

1

√

sec

2

θ

−

1
(ii)

√

sec

2

θ

−

1

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

1

sec

θ

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

cosec

θ
(ii)

1

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

√

cosec

2

θ

−

1

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

sin

θ

(ii)

1

sin

θ
(iii)

√

1

−

sin

2

θ

(iv)

sin

θ

√

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

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 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ
(ii)

1

cot

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

θ

√

sec

2

θ

−

1

(ii)

1

sec

θ

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1
(v)

1

√

sec

2

θ

−

1

Question 10

10.

Express
cos

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 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

1

sin

θ
(iii)

√

1

−

sin

2

θ
(iv)

1

√

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

cos

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

cos

θ
(iv)

√

1

−

cos

2

θ
(v)

1

√

1

−

cos

2

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

1

√

1

+

cot

2

θ
(iii)

√

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)

1

√

sec

2

θ

−

1
(ii)

1

sec

θ

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1
(v)

1

cosec

θ

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

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 18

18.

Express
cot

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)

1

tan

θ
(v)

tan

θ

√

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

sec

θ

(iii)

1

sec

θ
(iv)

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1
(ii)

1

cosec

θ

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 21

21.

Express
sec

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 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ
(ii)

1

cos

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

√

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

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

√

1

+

tan

2

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)

1

cot

θ
(iv)

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

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

2

θ

sin

θ

(ii)

1

√

1

−

sin

2

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ
(v)

√

1

−

sin

2

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)

√

1

+

tan

2

θ

tan

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

1

tan

θ
(v)

√

1

+

tan

2

θ

Question 29

29.

Express
cosec

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)

cot

θ

√

1

+

cot

2

θ

(v)

1

cot

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

1

sec

θ
(iii)

√

sec

2

θ

−

1
(iv)

1

√

sec

2

θ

−

1

(v)

sec

θ

√

sec

2

θ

−

1

Question 31

31.

Express
sin

21°
in terms of
cos

21°

(i)

1

cos

21°

(ii)

cos

21°

√

1

−

cos

2

21°

(iii)

√

1

−

cos

2

21°

(iv)

√

1

−

cos

2

21°

cos

21°

(v)

1

√

1

−

cos

2

21°

Question 32

32.

Express
sin

63°
in terms of
tan

63°

(i)

√

1

+

tan

2

63°

tan

63°

(ii)

tan

63°

√

1

+

tan

2

63°

(iii)

1

√

1

+

tan

2

63°
(iv)

1

tan

63°
(v)

√

1

+

tan

2

63°

Question 33

33.

Express
sin

36°
in terms of
cot

36°

(i)

1

cot

36°

(ii)

cot

36°

√

1

+

cot

2

36°

(iii)

√

1

+

cot

2

36°
(iv)

1

√

1

+

cot

2

36°

(v)

√

1

+

cot

2

36°

cot

36°

Question 34

34.

Express
sin

32°
in terms of
sec

32°

(i)

√

sec

2

32°

−

1
(ii)

1

√

sec

2

32°

−

1

(iii)

sec

32°

√

sec

2

32°

−

1

(iv)

1

sec

32°

(v)

√

sec

2

32°

−

1

sec

32°

Question 35

35.

Express
sin

56°
in terms of
cosec

56°

(i)

√

cosec

2

56°

−

1

cosec

56°

(ii)

√

cosec

2

56°

−

1

(iii)

cosec

56°

√

cosec

2

56°

−

1

(iv)

1

√

cosec

2

56°

−

1
(v)

1

cosec

56°

Question 36

36.

Express
cos

25°
in terms of
sin

25°

(i)

1

sin

25°
(ii)

1

√

1

−

sin

2

25°

(iii)

√

1

−

sin

2

25°

sin

25°

(iv)

√

1

−

sin

2

25°

(v)

sin

25°

√

1

−

sin

2

25°

Question 37

37.

Express
cos

56°
in terms of
tan

56°

(i)

1

tan

56°
(ii)

1

√

1

+

tan

2

56°
(iii)

√

1

+

tan

2

56°

(iv)

√

1

+

tan

2

56°

tan

56°

(v)

tan

56°

√

1

+

tan

2

56°

Question 38

38.

Express
cos

52°
in terms of
cot

52°

(i)

1

cot

52°

(ii)

√

1

+

cot

2

52°

cot

52°

(iii)

cot

52°

√

1

+

cot

2

52°

(iv)

√

1

+

cot

2

52°
(v)

1

√

1

+

cot

2

52°

Question 39

39.

Express
cos

75°
in terms of
sec

75°

(i)

√

sec

2

75°

−

1

(ii)

√

sec

2

75°

−

1

sec

75°

(iii)

1

√

sec

2

75°

−

1
(iv)

1

sec

75°

(v)

sec

75°

√

sec

2

75°

−

1

Question 40

40.

Express
cos

53°
in terms of
cosec

53°

(i)

√

cosec

2

53°

−

1

(ii)

√

cosec

2

53°

−

1

cosec

53°

(iii)

1

√

cosec

2

53°

−

1
(iv)

1

cosec

53°

(v)

cosec

53°

√

cosec

2

53°

−

1

Question 41

41.

Express
tan

46°
in terms of
sin

46°

(i)

1

sin

46°
(ii)

√

1

−

sin

2

46°

(iii)

sin

46°

√

1

−

sin

2

46°

(iv)

√

1

−

sin

2

46°

sin

46°

(v)

1

√

1

−

sin

2

46°

Question 42

42.

Express
tan

33°
in terms of
cos

33°

(i)

1

√

1

−

cos

2

33°
(ii)

√

1

−

cos

2

33°

(iii)

cos

33°

√

1

−

cos

2

33°

(iv)

√

1

−

cos

2

33°

cos

33°

(v)

1

cos

33°

Question 43

43.

Express
tan

51°
in terms of
cot

51°

(i)

√

1

+

cot

2

51°

(ii)

cot

51°

√

1

+

cot

2

51°

(iii)

√

1

+

cot

2

51°

cot

51°

(iv)

1

cot

51°
(v)

1

√

1

+

cot

2

51°

Question 44

44.

Express
tan

35°
in terms of
sec

35°

(i)

1

sec

35°

(ii)

√

sec

2

35°

−

1

sec

35°

(iii)

sec

35°

√

sec

2

35°

−

1

(iv)

1

√

sec

2

35°

−

1
(v)

√

sec

2

35°

−

1

Question 45

45.

Express
tan

51°
in terms of
cosec

51°

(i)

1

√

cosec

2

51°

−

1
(ii)

√

cosec

2

51°

−

1

(iii)

√

cosec

2

51°

−

1

cosec

51°

(iv)

1

cosec

51°

(v)

cosec

51°

√

cosec

2

51°

−

1

Question 46

46.

Express
cot

56°
in terms of
sin

56°

(i)

sin

56°

√

1

−

sin

2

56°

(ii)

1

√

1

−

sin

2

56°
(iii)

√

1

−

sin

2

56°

(iv)

√

1

−

sin

2

56°

sin

56°

(v)

1

sin

56°

Question 47

47.

Express
cot

24°
in terms of
cos

24°

(i)

1

√

1

−

cos

2

24°

(ii)

√

1

−

cos

2

24°

cos

24°

(iii)

1

cos

24°

(iv)

cos

24°

√

1

−

cos

2

24°

(v)

√

1

−

cos

2

24°

Question 48

48.

Express
cot

35°
in terms of
tan

35°

(i)

tan

35°

√

1

+

tan

2

35°

(ii)

√

1

+

tan

2

35°

tan

35°

(iii)

√

1

+

tan

2

35°
(iv)

1

√

1

+

tan

2

35°
(v)

1

tan

35°

Question 49

49.

Express
cot

64°
in terms of
sec

64°

(i)

sec

64°

√

sec

2

64°

−

1

(ii)

1

sec

64°
(iii)

√

sec

2

64°

−

1
(iv)

1

√

sec

2

64°

−

1

(v)

√

sec

2

64°

−

1

sec

64°

Question 50

50.

Express
cot

61°
in terms of
cosec

61°

(i)

√

cosec

2

61°

−

1

(ii)

√

cosec

2

61°

−

1

cosec

61°

(iii)

1

√

cosec

2

61°

−

1
(iv)

1

cosec

61°

(v)

cosec

61°

√

cosec

2

61°

−

1

Question 51

51.

Express
sec

63°
in terms of
sin

63°

(i)

1

√

1

−

sin

2

63°
(ii)

√

1

−

sin

2

63°
(iii)

1

sin

63°

(iv)

√

1

−

sin

2

63°

sin

63°

(v)

sin

63°

√

1

−

sin

2

63°

Question 52

52.

Express
sec

30°
in terms of
cos

30°

(i)

√

1

−

cos

2

30°

(ii)

cos

30°

√

1

−

cos

2

30°

(iii)

1

cos

30°
(iv)

1

√

1

−

cos

2

30°

(v)

√

1

−

cos

2

30°

cos

30°

Question 53

53.

Express
sec

52°
in terms of
tan

52°

(i)

1

√

1

+

tan

2

52°

(ii)

tan

52°

√

1

+

tan

2

52°

(iii)

√

1

+

tan

2

52°

(iv)

√

1

+

tan

2

52°

tan

52°

(v)

1

tan

52°

Question 54

54.

Express
sec

28°
in terms of
cot

28°

(i)

1

√

1

+

cot

2

28°

(ii)

cot

28°

√

1

+

cot

2

28°

(iii)

1

cot

28°

(iv)

√

1

+

cot

2

28°

cot

28°

(v)

√

1

+

cot

2

28°

Question 55

55.

Express
sec

79°
in terms of
cosec

79°

(i)

cosec

79°

√

cosec

2

79°

−

1

(ii)

1

cosec

79°
(iii)

√

cosec

2

79°

−

1

(iv)

√

cosec

2

79°

−

1

cosec

79°

(v)

1

√

cosec

2

79°

−

1

Question 56

56.

Express
cosec

34°
in terms of
sin

34°

(i)

1

√

1

−

sin

2

34°
(ii)

1

sin

34°

(iii)

sin

34°

√

1

−

sin

2

34°

(iv)

√

1

−

sin

2

34°

(v)

√

1

−

sin

2

34°

sin

34°

Question 57

57.

Express
cosec

24°
in terms of
cos

24°

(i)

cos

24°

√

1

−

cos

2

24°

(ii)

1

cos

24°
(iii)

1

√

1

−

cos

2

24°

(iv)

√

1

−

cos

2

24°

cos

24°

(v)

√

1

−

cos

2

24°

Question 58

58.

Express
cosec

34°
in terms of
tan

34°

(i)

√

1

+

tan

2

34°

(ii)

√

1

+

tan

2

34°

tan

34°

(iii)

1

tan

34°
(iv)

1

√

1

+

tan

2

34°

(v)

tan

34°

√

1

+

tan

2

34°

Question 59

59.

Express
cosec

67°
in terms of
cot

67°

(i)

√

1

+

cot

2

67°

cot

67°

(ii)

cot

67°

√

1

+

cot

2

67°

(iii)

1

cot

67°
(iv)

1

√

1

+

cot

2

67°
(v)

√

1

+

cot

2

67°

Question 60

60.

Express
cosec

79°
in terms of
sec

79°

(i)

1

√

sec

2

79°

−

1
(ii)

√

sec

2

79°

−

1
(iii)

1

sec

79°

(iv)

sec

79°

√

sec

2

79°

−

1

(v)

√

sec

2

79°

−

1

sec

79°

Assignment Key