24. If sin 0 = a, and tan 0=b, prove that

Express the following functions in terms of the functions

of acute angles less than 45°:

35. tan 1020°, sec 1395°, sin 1485°.

1

−√3, √2,

36. sin (-240°), cot (— 675°), cosec (— 690°).

37. cos (-300°), cot (-315°), cosec (-1740°).

38. tan3 660°, cos3 1020°.

Find the value of the sine, cosine, and tangent of the

Prove, drawing a separate figure in each case, that

46. sin 340° sin (-160°).

=

57. Can an angle be drawn whose tangent is 427?

60. Find four angles between zero and +8 right angles which satisfy the equations

61. State the sign of the sine, cosine, and tangent of each

of the following angles :

(1) 275°; (2) − 91°; (3) — 193°; (4) — 350°;

Prove the following identities:

62. (sin2+cos20) 1.

63. (sin20cos20)21-4 cos20+4 cos* 0.

66. (cosec

0

cot 0) (cosec + cot 0) = 1.

67. sin30+ cos3 0 = (sin 0 + cos 0) (1 − sin cos 0).

68. sin0+ coso 0 = sin10 + cos10 — sin2 0 cos2 0.

69. sin20 tan20+ cos20 cot20 tan20+ cot20 -1.

70. sin 0 tan20+ coseco sec20= 2 tan 0 sec0- cosec0+ sin 0.

71. cos30 - sin30 = (cos 0 — sin 0) (1 + sin cos 0).

73. tana+tan ß= tan a tan ẞ (cota + cot B).

74. cota +tan ß cot a tan ẞ (tan a + cot ẞ).

75. 1 sin a

α = (1 + sina) (sec α — - tan).

76. 1+ cos α =

(1

cos α) (cosecα- cotα).

77. (1+sina + cos a)2= 2(1 + sina) (1 + cos α).

78. (1-sina - cos a)(1 + sin a+ cos a)2= 4 sin2 a cos2α. · cosα)2=

79. 2 vers a vers2 α = sin'α.

80. versa (1+ cos α) = sin2α.