EduSahara™ Worksheet

EduSahara™ Assignment

Name : Trigonometric ratios in terms of other ratios

Chapter : Trigonometrical Identities

Grade : ICSE Grade X

License : Non Commercial Use

Question 1

1.

Express
sin

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

1

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

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

√

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)

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 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

cosec

θ
(ii)

√

cosec

2

θ

−

1
(iii)

1

√

cosec

2

θ

−

1

(iv)

√

cosec

2

θ

−

1

cosec

θ

(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)

sin

θ

√

1

−

sin

2

θ

(iii)

1

√

1

−

sin

2

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

tan

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

√

1

+

tan

2

θ
(v)

1

tan

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ
(ii)

1

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

1

√

1

+

cot

2

θ

Question 9

9.

Express
cos

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 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

θ
(ii)

1

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

√

1

−

sin

2

θ

(v)

sin

θ

√

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)

1

cos

θ
(iv)

1

√

1

−

cos

2

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ
(iv)

1

cot

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

θ

√

sec

2

θ

−

1

(iii)

1

sec

θ

(iv)

√

sec

2

θ

−

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

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(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)

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

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

1

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

Question 18

18.

Express
cot

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

tan

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

√

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

θ

√

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

θ

(iii)

√

cosec

2

θ

−

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)

sin

θ

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

1

√

1

−

sin

2

θ
(v)

1

sin

θ

Question 22

22.

Express
sec

θ
in terms of
cos

θ

(i)

1

cos

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

√

1

−

cos

2

θ
(v)

1

√

1

−

cos

2

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

1

tan

θ
(ii)

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

√

1

+

tan

2

θ

Question 24

24.

Express
sec

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

cot

θ

(v)

√

1

+

cot

2

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)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ
(v)

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

1

√

1

−

sin

2

θ
(iii)

1

sin

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

√

1

−

sin

2

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ
(ii)

1

cos

θ
(iii)

1

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 28

28.

Express
cosec

θ
in terms of
tan

θ

(i)

1

tan

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

√

1

+

tan

2

θ

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

tan

θ

√

1

+

tan

2

θ

Question 29

29.

Express
cosec

θ
in terms of
cot

θ

(i)

1

cot

θ

(ii)

√

1

+

cot

2

θ

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)

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 31

31.

Express
sin

25°
in terms of
cos

25°

(i)

cos

25°

√

1

−

cos

2

25°

(ii)

√

1

−

cos

2

25°

cos

25°

(iii)

√

1

−

cos

2

25°
(iv)

1

cos

25°
(v)

1

√

1

−

cos

2

25°

Question 32

32.

Express
sin

66°
in terms of
tan

66°

(i)

1

tan

66°
(ii)

1

√

1

+

tan

2

66°

(iii)

√

1

+

tan

2

66°

tan

66°

(iv)

√

1

+

tan

2

66°

(v)

tan

66°

√

1

+

tan

2

66°

Question 33

33.

Express
sin

52°
in terms of
cot

52°

(i)

√

1

+

cot

2

52°

cot

52°

(ii)

1

√

1

+

cot

2

52°
(iii)

1

cot

52°
(iv)

√

1

+

cot

2

52°

(v)

cot

52°

√

1

+

cot

2

52°

Question 34

34.

Express
sin

76°
in terms of
sec

76°

(i)

√

sec

2

76°

−

1

sec

76°

(ii)

1

√

sec

2

76°

−

1

(iii)

sec

76°

√

sec

2

76°

−

1

(iv)

1

sec

76°
(v)

√

sec

2

76°

−

1

Question 35

35.

Express
sin

62°
in terms of
cosec

62°

(i)

1

√

cosec

2

62°

−

1

(ii)

√

cosec

2

62°

−

1

cosec

62°

(iii)

cosec

62°

√

cosec

2

62°

−

1

(iv)

√

cosec

2

62°

−

1
(v)

1

cosec

62°

Question 36

36.

Express
cos

32°
in terms of
sin

32°

(i)

sin

32°

√

1

−

sin

2

32°

(ii)

1

sin

32°
(iii)

1

√

1

−

sin

2

32°

(iv)

√

1

−

sin

2

32°

sin

32°

(v)

√

1

−

sin

2

32°

Question 37

37.

Express
cos

71°
in terms of
tan

71°

(i)

√

1

+

tan

2

71°

tan

71°

(ii)

√

1

+

tan

2

71°

(iii)

tan

71°

√

1

+

tan

2

71°

(iv)

1

√

1

+

tan

2

71°
(v)

1

tan

71°

Question 38

38.

Express
cos

76°
in terms of
cot

76°

(i)

1

cot

76°
(ii)

1

√

1

+

cot

2

76°
(iii)

√

1

+

cot

2

76°

(iv)

√

1

+

cot

2

76°

cot

76°

(v)

cot

76°

√

1

+

cot

2

76°

Question 39

39.

Express
cos

42°
in terms of
sec

42°

(i)

√

sec

2

42°

−

1

sec

42°

(ii)

sec

42°

√

sec

2

42°

−

1

(iii)

√

sec

2

42°

−

1
(iv)

1

sec

42°
(v)

1

√

sec

2

42°

−

1

Question 40

40.

Express
cos

28°
in terms of
cosec

28°

(i)

√

cosec

2

28°

−

1

cosec

28°

(ii)

cosec

28°

√

cosec

2

28°

−

1

(iii)

1

cosec

28°
(iv)

1

√

cosec

2

28°

−

1
(v)

√

cosec

2

28°

−

1

Question 41

41.

Express
tan

30°
in terms of
sin

30°

(i)

√

1

−

sin

2

30°

(ii)

√

1

−

sin

2

30°

sin

30°

(iii)

1

√

1

−

sin

2

30°
(iv)

1

sin

30°

(v)

sin

30°

√

1

−

sin

2

30°

Question 42

42.

Express
tan

27°
in terms of
cos

27°

(i)

1

cos

27°
(ii)

1

√

1

−

cos

2

27°

(iii)

√

1

−

cos

2

27°

cos

27°

(iv)

√

1

−

cos

2

27°

(v)

cos

27°

√

1

−

cos

2

27°

Question 43

43.

Express
tan

63°
in terms of
cot

63°

(i)

1

√

1

+

cot

2

63°
(ii)

1

cot

63°

(iii)

cot

63°

√

1

+

cot

2

63°

(iv)

√

1

+

cot

2

63°

(v)

√

1

+

cot

2

63°

cot

63°

Question 44

44.

Express
tan

38°
in terms of
sec

38°

(i)

sec

38°

√

sec

2

38°

−

1

(ii)

1

√

sec

2

38°

−

1
(iii)

1

sec

38°

(iv)

√

sec

2

38°

−

1

sec

38°

(v)

√

sec

2

38°

−

1

Question 45

45.

Express
tan

80°
in terms of
cosec

80°

(i)

1

cosec

80°

(ii)

√

cosec

2

80°

−

1

cosec

80°

(iii)

cosec

80°

√

cosec

2

80°

−

1

(iv)

√

cosec

2

80°

−

1
(v)

1

√

cosec

2

80°

−

1

Question 46

46.

Express
cot

65°
in terms of
sin

65°

(i)

√

1

−

sin

2

65°

sin

65°

(ii)

√

1

−

sin

2

65°
(iii)

1

sin

65°

(iv)

sin

65°

√

1

−

sin

2

65°

(v)

1

√

1

−

sin

2

65°

Question 47

47.

Express
cot

61°
in terms of
cos

61°

(i)

1

cos

61°
(ii)

1

√

1

−

cos

2

61°

(iii)

√

1

−

cos

2

61°

cos

61°

(iv)

cos

61°

√

1

−

cos

2

61°

(v)

√

1

−

cos

2

61°

Question 48

48.

Express
cot

39°
in terms of
tan

39°

(i)

tan

39°

√

1

+

tan

2

39°

(ii)

√

1

+

tan

2

39°

(iii)

√

1

+

tan

2

39°

tan

39°

(iv)

1

tan

39°
(v)

1

√

1

+

tan

2

39°

Question 49

49.

Express
cot

75°
in terms of
sec

75°

(i)

1

sec

75°

(ii)

sec

75°

√

sec

2

75°

−

1

(iii)

√

sec

2

75°

−

1

sec

75°

(iv)

1

√

sec

2

75°

−

1
(v)

√

sec

2

75°

−

1

Question 50

50.

Express
cot

60°
in terms of
cosec

60°

(i)

cosec

60°

√

cosec

2

60°

−

1

(ii)

1

√

cosec

2

60°

−

1

(iii)

√

cosec

2

60°

−

1

cosec

60°

(iv)

1

cosec

60°
(v)

√

cosec

2

60°

−

1

Question 51

51.

Express
sec

26°
in terms of
sin

26°

(i)

√

1

−

sin

2

26°
(ii)

1

√

1

−

sin

2

26°
(iii)

1

sin

26°

(iv)

√

1

−

sin

2

26°

sin

26°

(v)

sin

26°

√

1

−

sin

2

26°

Question 52

52.

Express
sec

74°
in terms of
cos

74°

(i)

√

1

−

cos

2

74°

(ii)

√

1

−

cos

2

74°

cos

74°

(iii)

cos

74°

√

1

−

cos

2

74°

(iv)

1

√

1

−

cos

2

74°
(v)

1

cos

74°

Question 53

53.

Express
sec

53°
in terms of
tan

53°

(i)

1

√

1

+

tan

2

53°
(ii)

1

tan

53°
(iii)

√

1

+

tan

2

53°

(iv)

√

1

+

tan

2

53°

tan

53°

(v)

tan

53°

√

1

+

tan

2

53°

Question 54

54.

Express
sec

70°
in terms of
cot

70°

(i)

√

1

+

cot

2

70°

cot

70°

(ii)

√

1

+

cot

2

70°
(iii)

1

√

1

+

cot

2

70°

(iv)

cot

70°

√

1

+

cot

2

70°

(v)

1

cot

70°

Question 55

55.

Express
sec

76°
in terms of
cosec

76°

(i)

√

cosec

2

76°

−

1
(ii)

1

cosec

76°

(iii)

cosec

76°

√

cosec

2

76°

−

1

(iv)

1

√

cosec

2

76°

−

1

(v)

√

cosec

2

76°

−

1

cosec

76°

Question 56

56.

Express
cosec

29°
in terms of
sin

29°

(i)

1

sin

29°
(ii)

√

1

−

sin

2

29°
(iii)

1

√

1

−

sin

2

29°

(iv)

√

1

−

sin

2

29°

sin

29°

(v)

sin

29°

√

1

−

sin

2

29°

Question 57

57.

Express
cosec

33°
in terms of
cos

33°

(i)

1

cos

33°
(ii)

√

1

−

cos

2

33°

(iii)

√

1

−

cos

2

33°

cos

33°

(iv)

cos

33°

√

1

−

cos

2

33°

(v)

1

√

1

−

cos

2

33°

Question 58

58.

Express
cosec

66°
in terms of
tan

66°

(i)

1

√

1

+

tan

2

66°
(ii)

√

1

+

tan

2

66°
(iii)

1

tan

66°

(iv)

tan

66°

√

1

+

tan

2

66°

(v)

√

1

+

tan

2

66°

tan

66°

Question 59

59.

Express
cosec

65°
in terms of
cot

65°

(i)

√

1

+

cot

2

65°

cot

65°

(ii)

1

√

1

+

cot

2

65°
(iii)

1

cot

65°

(iv)

cot

65°

√

1

+

cot

2

65°

(v)

√

1

+

cot

2

65°

Question 60

60.

Express
cosec

66°
in terms of
sec

66°

(i)

1

sec

66°

(ii)

sec

66°

√

sec

2

66°

−

1

(iii)

√

sec

2

66°

−

1

sec

66°

(iv)

1

√

sec

2

66°

−

1
(v)

√

sec

2

66°

−

1

Assignment Key