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

−

cos

2

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

1

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

1

cos

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

1

√

1

+

tan

2

θ
(ii)

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

tan

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 3

3.

Express
sin

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 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

1

√

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)

√

cosec

2

θ

−

1

cosec

θ

(ii)

√

cosec

2

θ

−

1

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ
(v)

1

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ
(ii)

1

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

1

sin

θ

(v)

sin

θ

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

1

tan

θ
(ii)

√

1

+

tan

2

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

1

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

tan

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

cot

θ

√

1

+

cot

2

θ
(ii)

1

cot

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

Question 9

9.

Express
cos

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1
(ii)

1

√

sec

2

θ

−

1
(iii)

1

sec

θ

(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)

1

√

cosec

2

θ

−

1

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ
(v)

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

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

2

θ
(v)

1

sin

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ
(ii)

1

cos

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

√

1

−

cos

2

θ

(v)

√

1

−

cos

2

θ

cos

θ

Question 13

13.

Express
tan

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

1

√

1

+

cot

2

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

√

1

+

cot

2

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

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

sec

θ

√

sec

2

θ

−

1

Question 15

15.

Express
tan

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 16

16.

Express
cot

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

−

sin

2

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

−

cos

2

θ

cos

θ

(iii)

1

√

1

−

cos

2

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

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

1

tan

θ
(v)

1

√

1

+

tan

2

θ

Question 19

19.

Express
cot

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 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

1

cosec

θ
(iii)

1

√

cosec

2

θ

−

1
(iv)

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 21

21.

Express
sec

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ
(ii)

1

sin

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

sin

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

2

θ

cos

θ

(iv)

1

cos

θ
(v)

1

√

1

−

cos

2

θ

Question 23

23.

Express
sec

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

√

1

+

tan

2

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

1

tan

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

1

cot

θ

(ii)

√

1

+

cot

2

θ

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1
(ii)

1

√

cosec

2

θ

−

1
(iii)

1

cosec

θ

(iv)

√

cosec

2

θ

−

1

cosec

θ

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

1

sin

θ

(ii)

sin

θ

√

1

−

sin

2

θ

(iii)

1

√

1

−

sin

2

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

θ

(ii)

√

1

−

cos

2

θ

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

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

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

√

1

+

cot

2

θ
(iv)

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

1

sec

θ
(ii)

1

√

sec

2

θ

−

1
(iii)

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

sec

θ

√

sec

2

θ

−

1

Question 31

31.

Express
sin

27°
in terms of
cos

27°

(i)

√

1

−

cos

2

27°

cos

27°

(ii)

cos

27°

√

1

−

cos

2

27°

(iii)

√

1

−

cos

2

27°
(iv)

1

cos

27°
(v)

1

√

1

−

cos

2

27°

Question 32

32.

Express
sin

41°
in terms of
tan

41°

(i)

tan

41°

√

1

+

tan

2

41°

(ii)

√

1

+

tan

2

41°
(iii)

1

√

1

+

tan

2

41°

(iv)

√

1

+

tan

2

41°

tan

41°

(v)

1

tan

41°

Question 33

33.

Express
sin

39°
in terms of
cot

39°

(i)

1

√

1

+

cot

2

39°
(ii)

√

1

+

cot

2

39°
(iii)

1

cot

39°

(iv)

cot

39°

√

1

+

cot

2

39°

(v)

√

1

+

cot

2

39°

cot

39°

Question 34

34.

Express
sin

60°
in terms of
sec

60°

(i)

1

√

sec

2

60°

−

1

(ii)

sec

60°

√

sec

2

60°

−

1

(iii)

√

sec

2

60°

−

1

sec

60°

(iv)

1

sec

60°
(v)

√

sec

2

60°

−

1

Question 35

35.

Express
sin

29°
in terms of
cosec

29°

(i)

1

√

cosec

2

29°

−

1
(ii)

√

cosec

2

29°

−

1

(iii)

√

cosec

2

29°

−

1

cosec

29°

(iv)

1

cosec

29°

(v)

cosec

29°

√

cosec

2

29°

−

1

Question 36

36.

Express
cos

68°
in terms of
sin

68°

(i)

1

√

1

−

sin

2

68°
(ii)

1

sin

68°

(iii)

√

1

−

sin

2

68°

sin

68°

(iv)

sin

68°

√

1

−

sin

2

68°

(v)

√

1

−

sin

2

68°

Question 37

37.

Express
cos

77°
in terms of
tan

77°

(i)

√

1

+

tan

2

77°
(ii)

1

√

1

+

tan

2

77°

(iii)

tan

77°

√

1

+

tan

2

77°

(iv)

1

tan

77°

(v)

√

1

+

tan

2

77°

tan

77°

Question 38

38.

Express
cos

64°
in terms of
cot

64°

(i)

√

1

+

cot

2

64°
(ii)

1

cot

64°

(iii)

√

1

+

cot

2

64°

cot

64°

(iv)

cot

64°

√

1

+

cot

2

64°

(v)

1

√

1

+

cot

2

64°

Question 39

39.

Express
cos

68°
in terms of
sec

68°

(i)

1

sec

68°

(ii)

sec

68°

√

sec

2

68°

−

1

(iii)

1

√

sec

2

68°

−

1

(iv)

√

sec

2

68°

−

1

sec

68°

(v)

√

sec

2

68°

−

1

Question 40

40.

Express
cos

51°
in terms of
cosec

51°

(i)

√

cosec

2

51°

−

1

cosec

51°

(ii)

1

√

cosec

2

51°

−

1
(iii)

1

cosec

51°

(iv)

cosec

51°

√

cosec

2

51°

−

1

(v)

√

cosec

2

51°

−

1

Question 41

41.

Express
tan

29°
in terms of
sin

29°

(i)

sin

29°

√

1

−

sin

2

29°

(ii)

1

sin

29°

(iii)

√

1

−

sin

2

29°

sin

29°

(iv)

√

1

−

sin

2

29°
(v)

1

√

1

−

sin

2

29°

Question 42

42.

Express
tan

70°
in terms of
cos

70°

(i)

1

√

1

−

cos

2

70°
(ii)

1

cos

70°

(iii)

√

1

−

cos

2

70°

cos

70°

(iv)

√

1

−

cos

2

70°

(v)

cos

70°

√

1

−

cos

2

70°

Question 43

43.

Express
tan

60°
in terms of
cot

60°

(i)

1

cot

60°
(ii)

1

√

1

+

cot

2

60°

(iii)

cot

60°

√

1

+

cot

2

60°

(iv)

√

1

+

cot

2

60°

(v)

√

1

+

cot

2

60°

cot

60°

Question 44

44.

Express
tan

74°
in terms of
sec

74°

(i)

1

sec

74°
(ii)

1

√

sec

2

74°

−

1

(iii)

sec

74°

√

sec

2

74°

−

1

(iv)

√

sec

2

74°

−

1

sec

74°

(v)

√

sec

2

74°

−

1

Question 45

45.

Express
tan

29°
in terms of
cosec

29°

(i)

1

cosec

29°

(ii)

√

cosec

2

29°

−

1

cosec

29°

(iii)

1

√

cosec

2

29°

−

1

(iv)

cosec

29°

√

cosec

2

29°

−

1

(v)

√

cosec

2

29°

−

1

Question 46

46.

Express
cot

56°
in terms of
sin

56°

(i)

√

1

−

sin

2

56°

sin

56°

(ii)

1

√

1

−

sin

2

56°

(iii)

sin

56°

√

1

−

sin

2

56°

(iv)

1

sin

56°
(v)

√

1

−

sin

2

56°

Question 47

47.

Express
cot

78°
in terms of
cos

78°

(i)

√

1

−

cos

2

78°
(ii)

1

cos

78°

(iii)

√

1

−

cos

2

78°

cos

78°

(iv)

1

√

1

−

cos

2

78°

(v)

cos

78°

√

1

−

cos

2

78°

Question 48

48.

Express
cot

72°
in terms of
tan

72°

(i)

tan

72°

√

1

+

tan

2

72°

(ii)

1

√

1

+

tan

2

72°

(iii)

√

1

+

tan

2

72°

tan

72°

(iv)

√

1

+

tan

2

72°
(v)

1

tan

72°

Question 49

49.

Express
cot

45°
in terms of
sec

45°

(i)

1

sec

45°

(ii)

sec

45°

√

sec

2

45°

−

1

(iii)

1

√

sec

2

45°

−

1
(iv)

√

sec

2

45°

−

1

(v)

√

sec

2

45°

−

1

sec

45°

Question 50

50.

Express
cot

26°
in terms of
cosec

26°

(i)

cosec

26°

√

cosec

2

26°

−

1

(ii)

√

cosec

2

26°

−

1
(iii)

1

√

cosec

2

26°

−

1
(iv)

1

cosec

26°

(v)

√

cosec

2

26°

−

1

cosec

26°

Question 51

51.

Express
sec

48°
in terms of
sin

48°

(i)

√

1

−

sin

2

48°

(ii)

sin

48°

√

1

−

sin

2

48°

(iii)

1

√

1

−

sin

2

48°
(iv)

1

sin

48°

(v)

√

1

−

sin

2

48°

sin

48°

Question 52

52.

Express
sec

65°
in terms of
cos

65°

(i)

1

cos

65°

(ii)

√

1

−

cos

2

65°

cos

65°

(iii)

√

1

−

cos

2

65°
(iv)

1

√

1

−

cos

2

65°

(v)

cos

65°

√

1

−

cos

2

65°

Question 53

53.

Express
sec

64°
in terms of
tan

64°

(i)

tan

64°

√

1

+

tan

2

64°

(ii)

1

√

1

+

tan

2

64°
(iii)

1

tan

64°

(iv)

√

1

+

tan

2

64°

tan

64°

(v)

√

1

+

tan

2

64°

Question 54

54.

Express
sec

63°
in terms of
cot

63°

(i)

cot

63°

√

1

+

cot

2

63°

(ii)

√

1

+

cot

2

63°

cot

63°

(iii)

√

1

+

cot

2

63°
(iv)

1

cot

63°
(v)

1

√

1

+

cot

2

63°

Question 55

55.

Express
sec

65°
in terms of
cosec

65°

(i)

1

√

cosec

2

65°

−

1

(ii)

√

cosec

2

65°

−

1

cosec

65°

(iii)

cosec

65°

√

cosec

2

65°

−

1

(iv)

1

cosec

65°
(v)

√

cosec

2

65°

−

1

Question 56

56.

Express
cosec

45°
in terms of
sin

45°

(i)

√

1

−

sin

2

45°

(ii)

√

1

−

sin

2

45°

sin

45°

(iii)

sin

45°

√

1

−

sin

2

45°

(iv)

1

sin

45°
(v)

1

√

1

−

sin

2

45°

Question 57

57.

Express
cosec

35°
in terms of
cos

35°

(i)

1

cos

35°
(ii)

1

√

1

−

cos

2

35°

(iii)

√

1

−

cos

2

35°

cos

35°

(iv)

√

1

−

cos

2

35°

(v)

cos

35°

√

1

−

cos

2

35°

Question 58

58.

Express
cosec

74°
in terms of
tan

74°

(i)

tan

74°

√

1

+

tan

2

74°

(ii)

√

1

+

tan

2

74°

(iii)

√

1

+

tan

2

74°

tan

74°

(iv)

1

tan

74°
(v)

1

√

1

+

tan

2

74°

Question 59

59.

Express
cosec

34°
in terms of
cot

34°

(i)

1

√

1

+

cot

2

34°

(ii)

cot

34°

√

1

+

cot

2

34°

(iii)

√

1

+

cot

2

34°

cot

34°

(iv)

1

cot

34°
(v)

√

1

+

cot

2

34°

Question 60

60.

Express
cosec

29°
in terms of
sec

29°

(i)

1

√

sec

2

29°

−

1

(ii)

√

sec

2

29°

−

1

sec

29°

(iii)

√

sec

2

29°

−

1
(iv)

1

sec

29°

(v)

sec

29°

√

sec

2

29°

−

1

Assignment Key