Can you please show me the steps:

Question

Derive the identity for sin 3x in terms of sin x.

Answer 1

sin(3x) = sin(2x + x)
= sin2x*cosx + cos2x*sinx
= 2sinx*cos^2x + (1-2sin^2x)*sinx
= 2(1-sin^2x)sinx + (1-2sin^2x)*sinx
etc.