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

√

1

−

cos

2

θ
(ii)

√

1

−

cos

2

θ
(iii)

1

cos

θ

(iv)

√

1

−

cos

2

θ

cos

θ

(v)

cos

θ

√

1

−

cos

2

θ

Question 2

2.

Express
sin

θ
in terms of
tan

θ

(i)

1

√

1

+

tan

2

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

tan

θ
(iv)

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

tan

θ

Question 3

3.

Express
sin

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

1

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

√

1

+

cot

2

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1
(ii)

1

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

1

sec

θ

(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

cosec

θ

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

√

cosec

2

θ

−

1
(v)

1

√

cosec

2

θ

−

1

Question 6

6.

Express
cos

θ
in terms of
sin

θ

(i)

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

θ

(iii)

sin

θ

√

1

−

sin

2

θ

(iv)

1

sin

θ
(v)

1

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

tan

θ

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

tan

θ
(v)

√

1

+

tan

2

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ

(ii)

√

1

+

cot

2

θ

cot

θ

(iii)

cot

θ

√

1

+

cot

2

θ

(iv)

1

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

(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

θ

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

1

√

cosec

2

θ

−

1

Question 11

11.

Express
tan

θ
in terms of
sin

θ

(i)

1

sin

θ
(ii)

√

1

−

sin

2

θ
(iii)

1

√

1

−

sin

2

θ

(iv)

sin

θ

√

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)

cot

θ

√

1

+

cot

2

θ

(iv)

1

√

1

+

cot

2

θ
(v)

√

1

+

cot

2

θ

Question 14

14.

Express
tan

θ
in terms of
sec

θ

(i)

1

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1
(iv)

1

sec

θ

(v)

√

sec

2

θ

−

1

sec

θ

Question 15

15.

Express
tan

θ
in terms of
cosec

θ

(i)

1

√

cosec

2

θ

−

1
(ii)

√

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

−

sin

2

θ

(ii)

√

1

−

sin

2

θ

sin

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

−

cos

2

θ

cos

θ

(ii)

√

1

−

cos

2

θ
(iii)

1

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

1

√

1

−

cos

2

θ

Question 18

18.

Express
cot

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ

tan

θ
(ii)

1

√

1

+

tan

2

θ

(iii)

tan

θ

√

1

+

tan

2

θ

(iv)

1

tan

θ
(v)

√

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

θ

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

1

cosec

θ

(ii)

√

cosec

2

θ

−

1

cosec

θ

(iii)

1

√

cosec

2

θ

−

1

(iv)

cosec

θ

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

Question 21

21.

Express
sec

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 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

√

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

(iv)

√

1

+

tan

2

θ

tan

θ

(v)

1

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

1

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

1

cot

θ

Question 25

25.

Express
sec

θ
in terms of
cosec

θ

(i)

1

cosec

θ
(ii)

1

√

cosec

2

θ

−

1

(iii)

cosec

θ

√

cosec

2

θ

−

1

(iv)

√

cosec

2

θ

−

1

(v)

√

cosec

2

θ

−

1

cosec

θ

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

1

sin

θ
(ii)

1

√

1

−

sin

2

θ

(iii)

√

1

−

sin

2

θ

sin

θ

(iv)

sin

θ

√

1

−

sin

2

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

tan

θ

(ii)

tan

θ

√

1

+

tan

2

θ

(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

θ
(v)

√

1

+

tan

2

θ

Question 29

29.

Express
cosec

θ
in terms of
cot

θ

(i)

1

√

1

+

cot

2

θ
(ii)

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

cot

θ

(iv)

1

cot

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

sec

θ

(ii)

1

√

sec

2

θ

−

1
(iii)

1

sec

θ

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

√

sec

2

θ

−

1

Question 31

31.

Express
sin

39°
in terms of
cos

39°

(i)

1

cos

39°

(ii)

cos

39°

√

1

−

cos

2

39°

(iii)

√

1

−

cos

2

39°

cos

39°

(iv)

√

1

−

cos

2

39°
(v)

1

√

1

−

cos

2

39°

Question 32

32.

Express
sin

77°
in terms of
tan

77°

(i)

tan

77°

√

1

+

tan

2

77°

(ii)

1

√

1

+

tan

2

77°

(iii)

√

1

+

tan

2

77°

tan

77°

(iv)

√

1

+

tan

2

77°
(v)

1

tan

77°

Question 33

33.

Express
sin

69°
in terms of
cot

69°

(i)

√

1

+

cot

2

69°

cot

69°

(ii)

1

√

1

+

cot

2

69°
(iii)

√

1

+

cot

2

69°
(iv)

1

cot

69°

(v)

cot

69°

√

1

+

cot

2

69°

Question 34

34.

Express
sin

50°
in terms of
sec

50°

(i)

√

sec

2

50°

−

1

sec

50°

(ii)

1

sec

50°

(iii)

sec

50°

√

sec

2

50°

−

1

(iv)

√

sec

2

50°

−

1
(v)

1

√

sec

2

50°

−

1

Question 35

35.

Express
sin

77°
in terms of
cosec

77°

(i)

1

√

cosec

2

77°

−

1

(ii)

cosec

77°

√

cosec

2

77°

−

1

(iii)

√

cosec

2

77°

−

1
(iv)

1

cosec

77°

(v)

√

cosec

2

77°

−

1

cosec

77°

Question 36

36.

Express
cos

27°
in terms of
sin

27°

(i)

√

1

−

sin

2

27°

sin

27°

(ii)

1

√

1

−

sin

2

27°
(iii)

1

sin

27°

(iv)

sin

27°

√

1

−

sin

2

27°

(v)

√

1

−

sin

2

27°

Question 37

37.

Express
cos

56°
in terms of
tan

56°

(i)

√

1

+

tan

2

56°

(ii)

√

1

+

tan

2

56°

tan

56°

(iii)

1

√

1

+

tan

2

56°

(iv)

tan

56°

√

1

+

tan

2

56°

(v)

1

tan

56°

Question 38

38.

Express
cos

69°
in terms of
cot

69°

(i)

1

√

1

+

cot

2

69°

(ii)

cot

69°

√

1

+

cot

2

69°

(iii)

√

1

+

cot

2

69°

cot

69°

(iv)

√

1

+

cot

2

69°
(v)

1

cot

69°

Question 39

39.

Express
cos

31°
in terms of
sec

31°

(i)

1

sec

31°

(ii)

√

sec

2

31°

−

1

sec

31°

(iii)

√

sec

2

31°

−

1

(iv)

sec

31°

√

sec

2

31°

−

1

(v)

1

√

sec

2

31°

−

1

Question 40

40.

Express
cos

24°
in terms of
cosec

24°

(i)

cosec

24°

√

cosec

2

24°

−

1

(ii)

√

cosec

2

24°

−

1

cosec

24°

(iii)

√

cosec

2

24°

−

1
(iv)

1

√

cosec

2

24°

−

1
(v)

1

cosec

24°

Question 41

41.

Express
tan

73°
in terms of
sin

73°

(i)

√

1

−

sin

2

73°

(ii)

sin

73°

√

1

−

sin

2

73°

(iii)

√

1

−

sin

2

73°

sin

73°

(iv)

1

sin

73°
(v)

1

√

1

−

sin

2

73°

Question 42

42.

Express
tan

35°
in terms of
cos

35°

(i)

√

1

−

cos

2

35°
(ii)

1

cos

35°

(iii)

cos

35°

√

1

−

cos

2

35°

(iv)

1

√

1

−

cos

2

35°

(v)

√

1

−

cos

2

35°

cos

35°

Question 43

43.

Express
tan

49°
in terms of
cot

49°

(i)

√

1

+

cot

2

49°

(ii)

cot

49°

√

1

+

cot

2

49°

(iii)

1

√

1

+

cot

2

49°

(iv)

√

1

+

cot

2

49°

cot

49°

(v)

1

cot

49°

Question 44

44.

Express
tan

79°
in terms of
sec

79°

(i)

1

sec

79°
(ii)

√

sec

2

79°

−

1
(iii)

1

√

sec

2

79°

−

1

(iv)

√

sec

2

79°

−

1

sec

79°

(v)

sec

79°

√

sec

2

79°

−

1

Question 45

45.

Express
tan

29°
in terms of
cosec

29°

(i)

cosec

29°

√

cosec

2

29°

−

1

(ii)

1

cosec

29°
(iii)

1

√

cosec

2

29°

−

1

(iv)

√

cosec

2

29°

−

1

cosec

29°

(v)

√

cosec

2

29°

−

1

Question 46

46.

Express
cot

45°
in terms of
sin

45°

(i)

√

1

−

sin

2

45°

(ii)

sin

45°

√

1

−

sin

2

45°

(iii)

1

sin

45°

(iv)

√

1

−

sin

2

45°

sin

45°

(v)

1

√

1

−

sin

2

45°

Question 47

47.

Express
cot

58°
in terms of
cos

58°

(i)

1

cos

58°

(ii)

√

1

−

cos

2

58°

cos

58°

(iii)

√

1

−

cos

2

58°
(iv)

1

√

1

−

cos

2

58°

(v)

cos

58°

√

1

−

cos

2

58°

Question 48

48.

Express
cot

48°
in terms of
tan

48°

(i)

tan

48°

√

1

+

tan

2

48°

(ii)

√

1

+

tan

2

48°

tan

48°

(iii)

1

√

1

+

tan

2

48°
(iv)

1

tan

48°
(v)

√

1

+

tan

2

48°

Question 49

49.

Express
cot

65°
in terms of
sec

65°

(i)

sec

65°

√

sec

2

65°

−

1

(ii)

√

sec

2

65°

−

1

sec

65°

(iii)

1

√

sec

2

65°

−

1
(iv)

√

sec

2

65°

−

1
(v)

1

sec

65°

Question 50

50.

Express
cot

23°
in terms of
cosec

23°

(i)

1

√

cosec

2

23°

−

1

(ii)

√

cosec

2

23°

−

1

cosec

23°

(iii)

cosec

23°

√

cosec

2

23°

−

1

(iv)

√

cosec

2

23°

−

1
(v)

1

cosec

23°

Question 51

51.

Express
sec

70°
in terms of
sin

70°

(i)

1

sin

70°
(ii)

1

√

1

−

sin

2

70°

(iii)

√

1

−

sin

2

70°

sin

70°

(iv)

sin

70°

√

1

−

sin

2

70°

(v)

√

1

−

sin

2

70°

Question 52

52.

Express
sec

54°
in terms of
cos

54°

(i)

1

√

1

−

cos

2

54°
(ii)

√

1

−

cos

2

54°
(iii)

1

cos

54°

(iv)

cos

54°

√

1

−

cos

2

54°

(v)

√

1

−

cos

2

54°

cos

54°

Question 53

53.

Express
sec

25°
in terms of
tan

25°

(i)

√

1

+

tan

2

25°

tan

25°

(ii)

√

1

+

tan

2

25°

(iii)

tan

25°

√

1

+

tan

2

25°

(iv)

1

√

1

+

tan

2

25°
(v)

1

tan

25°

Question 54

54.

Express
sec

40°
in terms of
cot

40°

(i)

√

1

+

cot

2

40°

cot

40°

(ii)

√

1

+

cot

2

40°

(iii)

cot

40°

√

1

+

cot

2

40°

(iv)

1

cot

40°
(v)

1

√

1

+

cot

2

40°

Question 55

55.

Express
sec

58°
in terms of
cosec

58°

(i)

cosec

58°

√

cosec

2

58°

−

1

(ii)

1

√

cosec

2

58°

−

1
(iii)

√

cosec

2

58°

−

1
(iv)

1

cosec

58°

(v)

√

cosec

2

58°

−

1

cosec

58°

Question 56

56.

Express
cosec

32°
in terms of
sin

32°

(i)

√

1

−

sin

2

32°

(ii)

sin

32°

√

1

−

sin

2

32°

(iii)

√

1

−

sin

2

32°

sin

32°

(iv)

1

√

1

−

sin

2

32°
(v)

1

sin

32°

Question 57

57.

Express
cosec

72°
in terms of
cos

72°

(i)

√

1

−

cos

2

72°

cos

72°

(ii)

√

1

−

cos

2

72°
(iii)

1

√

1

−

cos

2

72°

(iv)

cos

72°

√

1

−

cos

2

72°

(v)

1

cos

72°

Question 58

58.

Express
cosec

66°
in terms of
tan

66°

(i)

tan

66°

√

1

+

tan

2

66°

(ii)

√

1

+

tan

2

66°

tan

66°

(iii)

1

√

1

+

tan

2

66°
(iv)

√

1

+

tan

2

66°
(v)

1

tan

66°

Question 59

59.

Express
cosec

51°
in terms of
cot

51°

(i)

cot

51°

√

1

+

cot

2

51°

(ii)

1

√

1

+

cot

2

51°
(iii)

1

cot

51°
(iv)

√

1

+

cot

2

51°

(v)

√

1

+

cot

2

51°

cot

51°

Question 60

60.

Express
cosec

57°
in terms of
sec

57°

(i)

√

sec

2

57°

−

1
(ii)

1

√

sec

2

57°

−

1

(iii)

√

sec

2

57°

−

1

sec

57°

(iv)

sec

57°

√

sec

2

57°

−

1

(v)

1

sec

57°

Assignment Key