Question

√3 cosec 20° - sec 20° =

(A) 2

(B) 2 sin 20° / sin 40°

(C) 4

(D) 4 sin 20°/ sin 40°

Answer 1

√3 cosec 20° - sec 20°

= √3 . 1/sin 20° - 1/cos 20°

= (√3 . cos 20° - 1 . sin 20°)/(sin 20° . cos 20°) . 4/4


= 4 ((1/2 .√3) cos 20° - (1/2) . sin 20°)/(2 . sin 20° cos 20°)

= 4 (sin 60° cos 20° - cos 60° . sin 20°)/(sin (2 . 20°)

= 4 (sin (60 - 20)°)/sin 40°

= 4 . sin 40° / sin 40°

= 4