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

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

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)

tan

θ

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ
(iii)

√

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

√

1

+

cot

2

θ

(ii)

cot

θ

√

1

+

cot

2

θ

(iii)

√

1

+

cot

2

θ

(iv)

√

1

+

cot

2

θ

cot

θ

(v)

1

cot

θ

Question 4

4.

Express
sin

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1

(ii)

√

sec

2

θ

−

1

sec

θ

(iii)

sec

θ

√

sec

2

θ

−

1

(iv)

1

sec

θ
(v)

1

√

sec

2

θ

−

1

Question 5

5.

Express
sin

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1

(iii)

√

cosec

2

θ

−

1

cosec

θ

(iv)

1

√

cosec

2

θ

−

1
(v)

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

θ

(iv)

√

1

−

sin

2

θ

sin

θ

(v)

√

1

−

sin

2

θ

Question 7

7.

Express
cos

θ
in terms of
tan

θ

(i)

√

1

+

tan

2

θ
(ii)

1

√

1

+

tan

2

θ

(iii)

√

1

+

tan

2

θ

tan

θ

(iv)

1

tan

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 8

8.

Express
cos

θ
in terms of
cot

θ

(i)

√

1

+

cot

2

θ

cot

θ
(ii)

1

cot

θ
(iii)

1

√

1

+

cot

2

θ
(iv)

√

1

+

cot

2

θ
(v)

cot

θ

√

1

+

cot

2

θ

Question 9

9.

Express
cos

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 10

10.

Express
cos

θ
in terms of
cosec

θ

(i)

cosec

θ

√

cosec

2

θ

−

1

(ii)

√

cosec

2

θ

−

1
(iii)

1

√

cosec

2

θ

−

1
(iv)

1

cosec

θ

(v)

√

cosec

2

θ

−

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

√

1

−

sin

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

√

1

−

sin

2

θ

Question 12

12.

Express
tan

θ
in terms of
cos

θ

(i)

cos

θ

√

1

−

cos

2

θ

(ii)

√

1

−

cos

2

θ

cos

θ

(iii)

1

cos

θ
(iv)

1

√

1

−

cos

2

θ
(v)

√

1

−

cos

2

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
(ii)

1

sec

θ

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

sec

θ

√

sec

2

θ

−

1

(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

θ

√

cosec

2

θ

−

1

(iv)

1

cosec

θ

(v)

√

cosec

2

θ

−

1

cosec

θ

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

2

θ

(iv)

sin

θ

√

1

−

sin

2

θ

(v)

1

sin

θ

Question 17

17.

Express
cot

θ
in terms of
cos

θ

(i)

1

√

1

−

cos

2

θ
(ii)

√

1

−

cos

2

θ

(iii)

√

1

−

cos

2

θ

cos

θ

(iv)

cos

θ

√

1

−

cos

2

θ

(v)

1

cos

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)

1

√

sec

2

θ

−

1

(ii)

sec

θ

√

sec

2

θ

−

1

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

√

sec

2

θ

−

1
(v)

1

sec

θ

Question 20

20.

Express
cot

θ
in terms of
cosec

θ

(i)

√

cosec

2

θ

−

1

cosec

θ

(ii)

1

cosec

θ

(iii)

cosec

θ

√

cosec

2

θ

−

1

(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

−

sin

2

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

2

θ

(ii)

cos

θ

√

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)

√

1

+

tan

2

θ

tan

θ
(ii)

√

1

+

tan

2

θ
(iii)

1

tan

θ
(iv)

1

√

1

+

tan

2

θ
(v)

tan

θ

√

1

+

tan

2

θ

Question 24

24.

Express
sec

θ
in terms of
cot

θ

(i)

1

cot

θ
(ii)

√

1

+

cot

2

θ
(iii)

1

√

1

+

cot

2

θ

(iv)

cot

θ

√

1

+

cot

2

θ

(v)

√

1

+

cot

2

θ

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

2

θ

−

1

cosec

θ

(iv)

√

cosec

2

θ

−

1

(v)

cosec

θ

√

cosec

2

θ

−

1

Question 26

26.

Express
cosec

θ
in terms of
sin

θ

(i)

sin

θ

√

1

−

sin

2

θ

(ii)

√

1

−

sin

2

θ
(iii)

1

√

1

−

sin

2

θ
(iv)

1

sin

θ

(v)

√

1

−

sin

2

θ

sin

θ

Question 27

27.

Express
cosec

θ
in terms of
cos

θ

(i)

√

1

−

cos

2

θ

cos

θ

(ii)

√

1

−

cos

2

θ

(iii)

cos

θ

√

1

−

cos

2

θ

(iv)

1

√

1

−

cos

2

θ
(v)

1

cos

θ

Question 28

28.

Express
cosec

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 29

29.

Express
cosec

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

2

θ
(v)

1

cot

θ

Question 30

30.

Express
cosec

θ
in terms of
sec

θ

(i)

√

sec

2

θ

−

1
(ii)

1

sec

θ

(iii)

√

sec

2

θ

−

1

sec

θ

(iv)

sec

θ

√

sec

2

θ

−

1

(v)

1

√

sec

2

θ

−

1

Question 31

31.

Express
sin

33°
in terms of
cos

33°

(i)

√

1

−

cos

2

33°

cos

33°

(ii)

1

cos

33°

(iii)

cos

33°

√

1

−

cos

2

33°

(iv)

1

√

1

−

cos

2

33°
(v)

√

1

−

cos

2

33°

Question 32

32.

Express
sin

50°
in terms of
tan

50°

(i)

√

1

+

tan

2

50°
(ii)

1

tan

50°

(iii)

tan

50°

√

1

+

tan

2

50°

(iv)

1

√

1

+

tan

2

50°

(v)

√

1

+

tan

2

50°

tan

50°

Question 33

33.

Express
sin

74°
in terms of
cot

74°

(i)

1

√

1

+

cot

2

74°

(ii)

√

1

+

cot

2

74°

cot

74°

(iii)

1

cot

74°
(iv)

√

1

+

cot

2

74°

(v)

cot

74°

√

1

+

cot

2

74°

Question 34

34.

Express
sin

54°
in terms of
sec

54°

(i)

√

sec

2

54°

−

1

(ii)

sec

54°

√

sec

2

54°

−

1

(iii)

√

sec

2

54°

−

1

sec

54°

(iv)

1

√

sec

2

54°

−

1
(v)

1

sec

54°

Question 35

35.

Express
sin

44°
in terms of
cosec

44°

(i)

√

cosec

2

44°

−

1

(ii)

cosec

44°

√

cosec

2

44°

−

1

(iii)

1

cosec

44°

(iv)

√

cosec

2

44°

−

1

cosec

44°

(v)

1

√

cosec

2

44°

−

1

Question 36

36.

Express
cos

69°
in terms of
sin

69°

(i)

√

1

−

sin

2

69°

sin

69°

(ii)

1

sin

69°
(iii)

1

√

1

−

sin

2

69°

(iv)

sin

69°

√

1

−

sin

2

69°

(v)

√

1

−

sin

2

69°

Question 37

37.

Express
cos

27°
in terms of
tan

27°

(i)

tan

27°

√

1

+

tan

2

27°

(ii)

√

1

+

tan

2

27°

tan

27°

(iii)

1

tan

27°
(iv)

1

√

1

+

tan

2

27°
(v)

√

1

+

tan

2

27°

Question 38

38.

Express
cos

44°
in terms of
cot

44°

(i)

1

cot

44°

(ii)

√

1

+

cot

2

44°

cot

44°

(iii)

1

√

1

+

cot

2

44°
(iv)

√

1

+

cot

2

44°

(v)

cot

44°

√

1

+

cot

2

44°

Question 39

39.

Express
cos

31°
in terms of
sec

31°

(i)

1

sec

31°

(ii)

√

sec

2

31°

−

1

sec

31°

(iii)

sec

31°

√

sec

2

31°

−

1

(iv)

√

sec

2

31°

−

1
(v)

1

√

sec

2

31°

−

1

Question 40

40.

Express
cos

25°
in terms of
cosec

25°

(i)

√

cosec

2

25°

−

1

(ii)

cosec

25°

√

cosec

2

25°

−

1

(iii)

1

√

cosec

2

25°

−

1
(iv)

1

cosec

25°

(v)

√

cosec

2

25°

−

1

cosec

25°

Question 41

41.

Express
tan

48°
in terms of
sin

48°

(i)

1

√

1

−

sin

2

48°
(ii)

1

sin

48°

(iii)

√

1

−

sin

2

48°

sin

48°

(iv)

sin

48°

√

1

−

sin

2

48°

(v)

√

1

−

sin

2

48°

Question 42

42.

Express
tan

66°
in terms of
cos

66°

(i)

1

cos

66°
(ii)

1

√

1

−

cos

2

66°
(iii)

√

1

−

cos

2

66°

(iv)

√

1

−

cos

2

66°

cos

66°

(v)

cos

66°

√

1

−

cos

2

66°

Question 43

43.

Express
tan

43°
in terms of
cot

43°

(i)

1

√

1

+

cot

2

43°

(ii)

cot

43°

√

1

+

cot

2

43°

(iii)

√

1

+

cot

2

43°

cot

43°

(iv)

√

1

+

cot

2

43°
(v)

1

cot

43°

Question 44

44.

Express
tan

23°
in terms of
sec

23°

(i)

1

√

sec

2

23°

−

1

(ii)

sec

23°

√

sec

2

23°

−

1

(iii)

√

sec

2

23°

−

1

(iv)

√

sec

2

23°

−

1

sec

23°

(v)

1

sec

23°

Question 45

45.

Express
tan

30°
in terms of
cosec

30°

(i)

√

cosec

2

30°

−

1

cosec

30°

(ii)

√

cosec

2

30°

−

1
(iii)

1

cosec

30°

(iv)

cosec

30°

√

cosec

2

30°

−

1

(v)

1

√

cosec

2

30°

−

1

Question 46

46.

Express
cot

30°
in terms of
sin

30°

(i)

√

1

−

sin

2

30°

sin

30°

(ii)

sin

30°

√

1

−

sin

2

30°

(iii)

√

1

−

sin

2

30°
(iv)

1

sin

30°
(v)

1

√

1

−

sin

2

30°

Question 47

47.

Express
cot

57°
in terms of
cos

57°

(i)

√

1

−

cos

2

57°
(ii)

1

√

1

−

cos

2

57°

(iii)

cos

57°

√

1

−

cos

2

57°

(iv)

√

1

−

cos

2

57°

cos

57°

(v)

1

cos

57°

Question 48

48.

Express
cot

68°
in terms of
tan

68°

(i)

√

1

+

tan

2

68°
(ii)

1

tan

68°

(iii)

tan

68°

√

1

+

tan

2

68°

(iv)

1

√

1

+

tan

2

68°

(v)

√

1

+

tan

2

68°

tan

68°

Question 49

49.

Express
cot

79°
in terms of
sec

79°

(i)

1

√

sec

2

79°

−

1
(ii)

1

sec

79°

(iii)

sec

79°

√

sec

2

79°

−

1

(iv)

√

sec

2

79°

−

1

sec

79°

(v)

√

sec

2

79°

−

1

Question 50

50.

Express
cot

24°
in terms of
cosec

24°

(i)

1

√

cosec

2

24°

−

1
(ii)

√

cosec

2

24°

−

1
(iii)

1

cosec

24°

(iv)

cosec

24°

√

cosec

2

24°

−

1

(v)

√

cosec

2

24°

−

1

cosec

24°

Question 51

51.

Express
sec

68°
in terms of
sin

68°

(i)

sin

68°

√

1

−

sin

2

68°

(ii)

√

1

−

sin

2

68°

sin

68°

(iii)

√

1

−

sin

2

68°
(iv)

1

√

1

−

sin

2

68°
(v)

1

sin

68°

Question 52

52.

Express
sec

52°
in terms of
cos

52°

(i)

1

cos

52°

(ii)

cos

52°

√

1

−

cos

2

52°

(iii)

1

√

1

−

cos

2

52°

(iv)

√

1

−

cos

2

52°

cos

52°

(v)

√

1

−

cos

2

52°

Question 53

53.

Express
sec

34°
in terms of
tan

34°

(i)

1

tan

34°
(ii)

√

1

+

tan

2

34°

(iii)

√

1

+

tan

2

34°

tan

34°

(iv)

tan

34°

√

1

+

tan

2

34°

(v)

1

√

1

+

tan

2

34°

Question 54

54.

Express
sec

54°
in terms of
cot

54°

(i)

cot

54°

√

1

+

cot

2

54°

(ii)

√

1

+

cot

2

54°
(iii)

1

cot

54°
(iv)

1

√

1

+

cot

2

54°

(v)

√

1

+

cot

2

54°

cot

54°

Question 55

55.

Express
sec

54°
in terms of
cosec

54°

(i)

1

√

cosec

2

54°

−

1
(ii)

1

cosec

54°

(iii)

√

cosec

2

54°

−

1

cosec

54°

(iv)

√

cosec

2

54°

−

1

(v)

cosec

54°

√

cosec

2

54°

−

1

Question 56

56.

Express
cosec

61°
in terms of
sin

61°

(i)

√

1

−

sin

2

61°

(ii)

√

1

−

sin

2

61°

sin

61°

(iii)

sin

61°

√

1

−

sin

2

61°

(iv)

1

√

1

−

sin

2

61°
(v)

1

sin

61°

Question 57

57.

Express
cosec

42°
in terms of
cos

42°

(i)

1

cos

42°
(ii)

√

1

−

cos

2

42°

(iii)

√

1

−

cos

2

42°

cos

42°

(iv)

1

√

1

−

cos

2

42°

(v)

cos

42°

√

1

−

cos

2

42°

Question 58

58.

Express
cosec

34°
in terms of
tan

34°

(i)

tan

34°

√

1

+

tan

2

34°

(ii)

√

1

+

tan

2

34°

tan

34°

(iii)

1

tan

34°
(iv)

√

1

+

tan

2

34°
(v)

1

√

1

+

tan

2

34°

Question 59

59.

Express
cosec

29°
in terms of
cot

29°

(i)

1

√

1

+

cot

2

29°

(ii)

√

1

+

cot

2

29°

cot

29°

(iii)

1

cot

29°

(iv)

cot

29°

√

1

+

cot

2

29°

(v)

√

1

+

cot

2

29°

Question 60

60.

Express
cosec

79°
in terms of
sec

79°

(i)

√

sec

2

79°

−

1

(ii)

sec

79°

√

sec

2

79°

−

1

(iii)

1

√

sec

2

79°

−

1
(iv)

1

sec

79°

(v)

√

sec

2

79°

−

1

sec

79°

Assignment Key