Question

If A = 30°;
show that:
sin 3 A = 4 sin A sin (60° - A) sin (60° + A)

Answer 1

Given that A = 30°

LHS = sin 3 A
= sin 3(30°)
= sin 90°
=1

RHS = 4 sin A sin (60° – A) sin (60° + A)

= 4 sin 30° sin ( 60° – 30°) sin (60° + 30°)

= `4(1/2)(1/2)(1)`

= 1

LHS = RHS