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

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 2

2.

Express
sin

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 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

cot

θ

√

1

+

cot

2

θ

(ii)

√

1

+

cot

2

θ

cot

θ

(iii)

1

cot

θ
(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

Question 4

4.

Express
sin

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 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1
(ii)

√

cosec

2

θ

−

1

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ

(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)

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

1

sin

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

√

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

√

1

+

cot

2

θ
(ii)

1

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

√

1

+

cot

2

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

θ

√

cosec

2

θ

−

1

(ii)

1

√

cosec

2

θ

−

1
(iii)

1

cosec

θ

(iv)

√

cosec

2

θ

−

1

cosec

θ

(v)

√

cosec

2

θ

−

1

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

θ
(ii)

√

1

−

cos

2

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

√

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

+

cot

2

θ

cot

θ

(iii)

√

1

+

cot

2

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

1

√

1

+

cot

2

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

1

sec

θ
(iv)

1

√

sec

2

θ

−

1
(v)

√

sec

2

θ

−

1

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

cosec

θ

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1
(iv)

1

√

cosec

2

θ

−

1
(v)

1

cosec

θ

Question 16

16.

Express
cot

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

sin

θ

(ii)

√

1

−

sin

2

θ
(iii)

1

sin

θ
(iv)

1

√

1

−

sin

2

θ

(v)

sin

θ

√

1

−

sin

2

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ
(ii)

1

cos

θ

(iii)

√

1

−

cos

2

θ

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

tan

θ
(ii)

1

tan

θ
(iii)

√

1

+

tan

2

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

θ

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1
(iii)

1

√

sec

2

θ

−

1

(iv)

√

sec

2

θ

−

1

sec

θ

(v)

1

sec

θ

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)

1

√

1

−

sin

2

θ
(ii)

1

sin

θ
(iii)

√

1

−

sin

2

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

θ

(ii)

cos

θ

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

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)

1

tan

θ

(ii)

√

1

+

tan

2

θ

tan

θ

(iii)

1

√

1

+

tan

2

θ

(iv)

tan

θ

√

1

+

tan

2

θ

(v)

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

cot

θ

√

1

+

cot

2

θ
(ii)

1

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

√

1

+

cot

2

θ
(v)

1

cot

θ

Question 25

25.

Express
sec

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)

√

cosec

2

θ

−

1
(v)

1

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

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

2

θ
(v)

1

sin

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ
(ii)

1

cos

θ
(iii)

√

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

+

tan

2

θ

tan

θ

(iii)

√

1

+

tan

2

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

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

1

cot

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

1

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

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 31

31.

Express
sin

59°
in terms of
cos

59°

(i)

√

1

−

cos

2

59°
(ii)

1

√

1

−

cos

2

59°

(iii)

√

1

−

cos

2

59°

cos

59°

(iv)

cos

59°

√

1

−

cos

2

59°

(v)

1

cos

59°

Question 32

32.

Express
sin

54°
in terms of
tan

54°

(i)

1

tan

54°
(ii)

1

√

1

+

tan

2

54°

(iii)

√

1

+

tan

2

54°

tan

54°

(iv)

√

1

+

tan

2

54°

(v)

tan

54°

√

1

+

tan

2

54°

Question 33

33.

Express
sin

34°
in terms of
cot

34°

(i)

√

1

+

cot

2

34°

cot

34°

(ii)

cot

34°

√

1

+

cot

2

34°

(iii)

√

1

+

cot

2

34°
(iv)

1

√

1

+

cot

2

34°
(v)

1

cot

34°

Question 34

34.

Express
sin

23°
in terms of
sec

23°

(i)

sec

23°

√

sec

2

23°

−

1

(ii)

√

sec

2

23°

−

1
(iii)

1

sec

23°

(iv)

√

sec

2

23°

−

1

sec

23°

(v)

1

√

sec

2

23°

−

1

Question 35

35.

Express
sin

27°
in terms of
cosec

27°

(i)

1

cosec

27°
(ii)

1

√

cosec

2

27°

−

1

(iii)

√

cosec

2

27°

−

1

cosec

27°

(iv)

cosec

27°

√

cosec

2

27°

−

1

(v)

√

cosec

2

27°

−

1

Question 36

36.

Express
cos

39°
in terms of
sin

39°

(i)

√

1

−

sin

2

39°

sin

39°

(ii)

1

sin

39°

(iii)

sin

39°

√

1

−

sin

2

39°

(iv)

1

√

1

−

sin

2

39°
(v)

√

1

−

sin

2

39°

Question 37

37.

Express
cos

51°
in terms of
tan

51°

(i)

√

1

+

tan

2

51°

tan

51°

(ii)

1

√

1

+

tan

2

51°

(iii)

tan

51°

√

1

+

tan

2

51°

(iv)

√

1

+

tan

2

51°
(v)

1

tan

51°

Question 38

38.

Express
cos

74°
in terms of
cot

74°

(i)

1

cot

74°
(ii)

√

1

+

cot

2

74°

(iii)

cot

74°

√

1

+

cot

2

74°

(iv)

√

1

+

cot

2

74°

cot

74°

(v)

1

√

1

+

cot

2

74°

Question 39

39.

Express
cos

22°
in terms of
sec

22°

(i)

sec

22°

√

sec

2

22°

−

1

(ii)

1

√

sec

2

22°

−

1
(iii)

1

sec

22°

(iv)

√

sec

2

22°

−

1

sec

22°

(v)

√

sec

2

22°

−

1

Question 40

40.

Express
cos

69°
in terms of
cosec

69°

(i)

cosec

69°

√

cosec

2

69°

−

1

(ii)

1

√

cosec

2

69°

−

1
(iii)

√

cosec

2

69°

−

1
(iv)

1

cosec

69°

(v)

√

cosec

2

69°

−

1

cosec

69°

Question 41

41.

Express
tan

74°
in terms of
sin

74°

(i)

1

sin

74°

(ii)

sin

74°

√

1

−

sin

2

74°

(iii)

√

1

−

sin

2

74°
(iv)

1

√

1

−

sin

2

74°

(v)

√

1

−

sin

2

74°

sin

74°

Question 42

42.

Express
tan

32°
in terms of
cos

32°

(i)

√

1

−

cos

2

32°
(ii)

1

√

1

−

cos

2

32°

(iii)

√

1

−

cos

2

32°

cos

32°

(iv)

1

cos

32°

(v)

cos

32°

√

1

−

cos

2

32°

Question 43

43.

Express
tan

73°
in terms of
cot

73°

(i)

√

1

+

cot

2

73°

cot

73°

(ii)

1

cot

73°
(iii)

√

1

+

cot

2

73°

(iv)

cot

73°

√

1

+

cot

2

73°

(v)

1

√

1

+

cot

2

73°

Question 44

44.

Express
tan

59°
in terms of
sec

59°

(i)

1

√

sec

2

59°

−

1

(ii)

√

sec

2

59°

−

1

sec

59°

(iii)

sec

59°

√

sec

2

59°

−

1

(iv)

1

sec

59°
(v)

√

sec

2

59°

−

1

Question 45

45.

Express
tan

64°
in terms of
cosec

64°

(i)

1

cosec

64°
(ii)

1

√

cosec

2

64°

−

1
(iii)

√

cosec

2

64°

−

1

(iv)

√

cosec

2

64°

−

1

cosec

64°

(v)

cosec

64°

√

cosec

2

64°

−

1

Question 46

46.

Express
cot

43°
in terms of
sin

43°

(i)

1

sin

43°
(ii)

1

√

1

−

sin

2

43°

(iii)

√

1

−

sin

2

43°

sin

43°

(iv)

sin

43°

√

1

−

sin

2

43°

(v)

√

1

−

sin

2

43°

Question 47

47.

Express
cot

75°
in terms of
cos

75°

(i)

√

1

−

cos

2

75°

cos

75°

(ii)

1

√

1

−

cos

2

75°

(iii)

cos

75°

√

1

−

cos

2

75°

(iv)

1

cos

75°
(v)

√

1

−

cos

2

75°

Question 48

48.

Express
cot

68°
in terms of
tan

68°

(i)

√

1

+

tan

2

68°

(ii)

√

1

+

tan

2

68°

tan

68°

(iii)

tan

68°

√

1

+

tan

2

68°

(iv)

1

tan

68°
(v)

1

√

1

+

tan

2

68°

Question 49

49.

Express
cot

23°
in terms of
sec

23°

(i)

sec

23°

√

sec

2

23°

−

1

(ii)

√

sec

2

23°

−

1

(iii)

√

sec

2

23°

−

1

sec

23°

(iv)

1

√

sec

2

23°

−

1
(v)

1

sec

23°

Question 50

50.

Express
cot

24°
in terms of
cosec

24°

(i)

√

cosec

2

24°

−

1
(ii)

1

√

cosec

2

24°

−

1

(iii)

cosec

24°

√

cosec

2

24°

−

1

(iv)

√

cosec

2

24°

−

1

cosec

24°

(v)

1

cosec

24°

Question 51

51.

Express
sec

28°
in terms of
sin

28°

(i)

√

1

−

sin

2

28°

(ii)

sin

28°

√

1

−

sin

2

28°

(iii)

1

sin

28°
(iv)

1

√

1

−

sin

2

28°

(v)

√

1

−

sin

2

28°

sin

28°

Question 52

52.

Express
sec

49°
in terms of
cos

49°

(i)

cos

49°

√

1

−

cos

2

49°

(ii)

√

1

−

cos

2

49°

cos

49°

(iii)

1

√

1

−

cos

2

49°
(iv)

√

1

−

cos

2

49°
(v)

1

cos

49°

Question 53

53.

Express
sec

51°
in terms of
tan

51°

(i)

1

tan

51°
(ii)

√

1

+

tan

2

51°

(iii)

tan

51°

√

1

+

tan

2

51°

(iv)

1

√

1

+

tan

2

51°

(v)

√

1

+

tan

2

51°

tan

51°

Question 54

54.

Express
sec

26°
in terms of
cot

26°

(i)

1

√

1

+

cot

2

26°
(ii)

1

cot

26°

(iii)

√

1

+

cot

2

26°

cot

26°

(iv)

cot

26°

√

1

+

cot

2

26°

(v)

√

1

+

cot

2

26°

Question 55

55.

Express
sec

56°
in terms of
cosec

56°

(i)

√

cosec

2

56°

−

1

(ii)

cosec

56°

√

cosec

2

56°

−

1

(iii)

√

cosec

2

56°

−

1

cosec

56°

(iv)

1

cosec

56°
(v)

1

√

cosec

2

56°

−

1

Question 56

56.

Express
cosec

44°
in terms of
sin

44°

(i)

1

√

1

−

sin

2

44°
(ii)

1

sin

44°

(iii)

sin

44°

√

1

−

sin

2

44°

(iv)

√

1

−

sin

2

44°

sin

44°

(v)

√

1

−

sin

2

44°

Question 57

57.

Express
cosec

48°
in terms of
cos

48°

(i)

1

√

1

−

cos

2

48°
(ii)

√

1

−

cos

2

48°
(iii)

1

cos

48°

(iv)

cos

48°

√

1

−

cos

2

48°

(v)

√

1

−

cos

2

48°

cos

48°

Question 58

58.

Express
cosec

53°
in terms of
tan

53°

(i)

1

tan

53°

(ii)

√

1

+

tan

2

53°

tan

53°

(iii)

√

1

+

tan

2

53°

(iv)

tan

53°

√

1

+

tan

2

53°

(v)

1

√

1

+

tan

2

53°

Question 59

59.

Express
cosec

48°
in terms of
cot

48°

(i)

1

cot

48°

(ii)

cot

48°

√

1

+

cot

2

48°

(iii)

√

1

+

cot

2

48°

cot

48°

(iv)

1

√

1

+

cot

2

48°
(v)

√

1

+

cot

2

48°

Question 60

60.

Express
cosec

62°
in terms of
sec

62°

(i)

sec

62°

√

sec

2

62°

−

1

(ii)

1

sec

62°

(iii)

√

sec

2

62°

−

1

sec

62°

(iv)

1

√

sec

2

62°

−

1
(v)

√

sec

2

62°

−

1

Assignment Key