Question

If A =30^o, then prove that :
sin 2A = 2sin A cos A =  `(2 tan"A")/(1 + tan^2"A")`

Answer 1

Given A = 30°

sin 2A = sin 2(30°) = sin60° = `(sqrt3)/(2)`

2sin A cos A = 2sin 30° cos 30°

= `2(1/2)(sqrt3/2)`

= `(sqrt3)/(2)`

`(2 tan"A")/(1 + tan^2 30°) = (2tan 30°)/(1 + tan^2 30°)`

= `(2(1/sqrt3))/(1 + (1/sqrt3)^2`

= `(2/sqrt3)/(4/(3)`

= `(2)/(sqrt3) xx (3)/(4)`

= `(sqrt3)/(2)`

∴ sin 2A = 2sin A cos A = `(2tan"A")/(1 + tan^2 "A")`