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

√

1

−

cos

2

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

cos

θ
(v)

√

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)

cot

θ

√

1

+

cot

2

θ

(iii)

1

cot

θ
(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

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)

1

√

sec

2

θ

−

1
(iv)

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

sec

θ

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

cosec

θ

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

1

√

cosec

2

θ

−

1
(iv)

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

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

√

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 8

8.

Express
cos

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 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

1

sec

θ
(ii)

√

sec

2

θ

−

1
(iii)

1

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

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)

cosec

θ

√

cosec

2

θ

−

1

(v)

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

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

1

√

1

−

sin

2

θ

Question 12

12.

Express
tan

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 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

1

cot

θ
(iv)

1

√

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

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)

1

cosec

θ
(ii)

1

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

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

sin

θ

(iii)

1

sin

θ
(iv)

√

1

−

sin

2

θ

(v)

sin

θ

√

1

−

sin

2

θ

Question 17

17.

Express
cot

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 18

18.

Express
cot

θ
in terms of
tan

θ

(i)

1

tan

θ
(ii)

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

√

1

+

tan

2

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 19

19.

Express
cot

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

√

sec

2

θ

−

1
(iii)

1

√

sec

2

θ

−

1
(iv)

1

sec

θ

(v)

sec

θ

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

1

cosec

θ
(iv)

1

√

cosec

2

θ

−

1
(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

θ
(v)

√

1

−

sin

2

θ

Question 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ
(iii)

1

cos

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

1

√

1

−

cos

2

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

1

tan

θ
(iv)

√

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)

1

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

cot

θ

√

1

+

cot

2

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

cosec

θ

(iii)

1

cosec

θ
(iv)

1

√

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)

sin

θ

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ
(iv)

1

sin

θ
(v)

1

√

1

−

sin

2

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

1

cos

θ
(ii)

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

1

√

1

−

cos

2

θ

Question 28

28.

Express
cosec

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

√

1

+

tan

2

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

θ
(iv)

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

cot

θ

Question 30

30.

Express
cosec

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 31

31.

Express
sin

72°
in terms of
cos

72°

(i)

cos

72°

√

1

−

cos

2

72°

(ii)

1

√

1

−

cos

2

72°
(iii)

√

1

−

cos

2

72°
(iv)

1

cos

72°

(v)

√

1

−

cos

2

72°

cos

72°

Question 32

32.

Express
sin

52°
in terms of
tan

52°

(i)

tan

52°

√

1

+

tan

2

52°

(ii)

√

1

+

tan

2

52°
(iii)

1

tan

52°

(iv)

√

1

+

tan

2

52°

tan

52°

(v)

1

√

1

+

tan

2

52°

Question 33

33.

Express
sin

66°
in terms of
cot

66°

(i)

√

1

+

cot

2

66°

(ii)

cot

66°

√

1

+

cot

2

66°

(iii)

1

cot

66°

(iv)

√

1

+

cot

2

66°

cot

66°

(v)

1

√

1

+

cot

2

66°

Question 34

34.

Express
sin

56°
in terms of
sec

56°

(i)

1

√

sec

2

56°

−

1

(ii)

sec

56°

√

sec

2

56°

−

1

(iii)

√

sec

2

56°

−

1

(iv)

√

sec

2

56°

−

1

sec

56°

(v)

1

sec

56°

Question 35

35.

Express
sin

51°
in terms of
cosec

51°

(i)

1

√

cosec

2

51°

−

1
(ii)

1

cosec

51°

(iii)

√

cosec

2

51°

−

1

cosec

51°

(iv)

√

cosec

2

51°

−

1

(v)

cosec

51°

√

cosec

2

51°

−

1

Question 36

36.

Express
cos

67°
in terms of
sin

67°

(i)

1

sin

67°

(ii)

sin

67°

√

1

−

sin

2

67°

(iii)

√

1

−

sin

2

67°

sin

67°

(iv)

1

√

1

−

sin

2

67°
(v)

√

1

−

sin

2

67°

Question 37

37.

Express
cos

65°
in terms of
tan

65°

(i)

1

tan

65°
(ii)

√

1

+

tan

2

65°

(iii)

tan

65°

√

1

+

tan

2

65°

(iv)

√

1

+

tan

2

65°

tan

65°

(v)

1

√

1

+

tan

2

65°

Question 38

38.

Express
cos

69°
in terms of
cot

69°

(i)

√

1

+

cot

2

69°

cot

69°

(ii)

√

1

+

cot

2

69°

(iii)

cot

69°

√

1

+

cot

2

69°

(iv)

1

cot

69°
(v)

1

√

1

+

cot

2

69°

Question 39

39.

Express
cos

51°
in terms of
sec

51°

(i)

√

sec

2

51°

−

1

sec

51°

(ii)

1

sec

51°
(iii)

√

sec

2

51°

−

1
(iv)

1

√

sec

2

51°

−

1

(v)

sec

51°

√

sec

2

51°

−

1

Question 40

40.

Express
cos

28°
in terms of
cosec

28°

(i)

√

cosec

2

28°

−

1

(ii)

cosec

28°

√

cosec

2

28°

−

1

(iii)

1

cosec

28°
(iv)

1

√

cosec

2

28°

−

1

(v)

√

cosec

2

28°

−

1

cosec

28°

Question 41

41.

Express
tan

28°
in terms of
sin

28°

(i)

1

sin

28°

(ii)

sin

28°

√

1

−

sin

2

28°

(iii)

√

1

−

sin

2

28°
(iv)

1

√

1

−

sin

2

28°

(v)

√

1

−

sin

2

28°

sin

28°

Question 42

42.

Express
tan

59°
in terms of
cos

59°

(i)

1

cos

59°
(ii)

1

√

1

−

cos

2

59°

(iii)

cos

59°

√

1

−

cos

2

59°

(iv)

√

1

−

cos

2

59°

(v)

√

1

−

cos

2

59°

cos

59°

Question 43

43.

Express
tan

50°
in terms of
cot

50°

(i)

1

cot

50°

(ii)

cot

50°

√

1

+

cot

2

50°

(iii)

√

1

+

cot

2

50°

cot

50°

(iv)

√

1

+

cot

2

50°
(v)

1

√

1

+

cot

2

50°

Question 44

44.

Express
tan

47°
in terms of
sec

47°

(i)

√

sec

2

47°

−

1
(ii)

1

sec

47°

(iii)

√

sec

2

47°

−

1

sec

47°

(iv)

sec

47°

√

sec

2

47°

−

1

(v)

1

√

sec

2

47°

−

1

Question 45

45.

Express
tan

41°
in terms of
cosec

41°

(i)

1

√

cosec

2

41°

−

1

(ii)

√

cosec

2

41°

−

1

cosec

41°

(iii)

1

cosec

41°
(iv)

√

cosec

2

41°

−

1

(v)

cosec

41°

√

cosec

2

41°

−

1

Question 46

46.

Express
cot

42°
in terms of
sin

42°

(i)

1

√

1

−

sin

2

42°
(ii)

√

1

−

sin

2

42°
(iii)

1

sin

42°

(iv)

√

1

−

sin

2

42°

sin

42°

(v)

sin

42°

√

1

−

sin

2

42°

Question 47

47.

Express
cot

40°
in terms of
cos

40°

(i)

√

1

−

cos

2

40°

(ii)

√

1

−

cos

2

40°

cos

40°

(iii)

1

√

1

−

cos

2

40°

(iv)

cos

40°

√

1

−

cos

2

40°

(v)

1

cos

40°

Question 48

48.

Express
cot

23°
in terms of
tan

23°

(i)

tan

23°

√

1

+

tan

2

23°

(ii)

1

tan

23°
(iii)

√

1

+

tan

2

23°

(iv)

√

1

+

tan

2

23°

tan

23°

(v)

1

√

1

+

tan

2

23°

Question 49

49.

Express
cot

35°
in terms of
sec

35°

(i)

√

sec

2

35°

−

1

sec

35°

(ii)

√

sec

2

35°

−

1
(iii)

1

sec

35°

(iv)

sec

35°

√

sec

2

35°

−

1

(v)

1

√

sec

2

35°

−

1

Question 50

50.

Express
cot

31°
in terms of
cosec

31°

(i)

1

cosec

31°

(ii)

cosec

31°

√

cosec

2

31°

−

1

(iii)

1

√

cosec

2

31°

−

1
(iv)

√

cosec

2

31°

−

1

(v)

√

cosec

2

31°

−

1

cosec

31°

Question 51

51.

Express
sec

36°
in terms of
sin

36°

(i)

√

1

−

sin

2

36°

sin

36°

(ii)

1

√

1

−

sin

2

36°
(iii)

1

sin

36°

(iv)

sin

36°

√

1

−

sin

2

36°

(v)

√

1

−

sin

2

36°

Question 52

52.

Express
sec

27°
in terms of
cos

27°

(i)

cos

27°

√

1

−

cos

2

27°

(ii)

√

1

−

cos

2

27°

(iii)

√

1

−

cos

2

27°

cos

27°

(iv)

1

√

1

−

cos

2

27°
(v)

1

cos

27°

Question 53

53.

Express
sec

79°
in terms of
tan

79°

(i)

1

√

1

+

tan

2

79°

(ii)

√

1

+

tan

2

79°

tan

79°

(iii)

√

1

+

tan

2

79°
(iv)

1

tan

79°

(v)

tan

79°

√

1

+

tan

2

79°

Question 54

54.

Express
sec

24°
in terms of
cot

24°

(i)

cot

24°

√

1

+

cot

2

24°

(ii)

1

cot

24°
(iii)

√

1

+

cot

2

24°
(iv)

1

√

1

+

cot

2

24°

(v)

√

1

+

cot

2

24°

cot

24°

Question 55

55.

Express
sec

36°
in terms of
cosec

36°

(i)

√

cosec

2

36°

−

1

cosec

36°

(ii)

√

cosec

2

36°

−

1
(iii)

1

cosec

36°
(iv)

1

√

cosec

2

36°

−

1

(v)

cosec

36°

√

cosec

2

36°

−

1

Question 56

56.

Express
cosec

65°
in terms of
sin

65°

(i)

1

√

1

−

sin

2

65°

(ii)

√

1

−

sin

2

65°

sin

65°

(iii)

√

1

−

sin

2

65°

(iv)

sin

65°

√

1

−

sin

2

65°

(v)

1

sin

65°

Question 57

57.

Express
cosec

23°
in terms of
cos

23°

(i)

1

cos

23°
(ii)

√

1

−

cos

2

23°
(iii)

1

√

1

−

cos

2

23°

(iv)

cos

23°

√

1

−

cos

2

23°

(v)

√

1

−

cos

2

23°

cos

23°

Question 58

58.

Express
cosec

55°
in terms of
tan

55°

(i)

tan

55°

√

1

+

tan

2

55°

(ii)

√

1

+

tan

2

55°
(iii)

1

tan

55°
(iv)

1

√

1

+

tan

2

55°

(v)

√

1

+

tan

2

55°

tan

55°

Question 59

59.

Express
cosec

65°
in terms of
cot

65°

(i)

√

1

+

cot

2

65°
(ii)

1

√

1

+

cot

2

65°
(iii)

1

cot

65°

(iv)

√

1

+

cot

2

65°

cot

65°

(v)

cot

65°

√

1

+

cot

2

65°

Question 60

60.

Express
cosec

32°
in terms of
sec

32°

(i)

1

sec

32°

(ii)

√

sec

2

32°

−

1

sec

32°

(iii)

1

√

sec

2

32°

−

1

(iv)

sec

32°

√

sec

2

32°

−

1

(v)

√

sec

2

32°

−

1

Assignment Key