Question

Prove:

Sin3theta = 3sintheta - 4 sin^3theta

I don't know where to start =/

Answer 1

Sin3x
= sin(x+2x)
= sinxcos2x + cosxsin2x
= sinx(1-2sin^2 x) + cosx(2sinxcosx)
= sinx - 2sin^3 x + 2sinxcos^2 x
= sinx - 2sin^3 x + 2sinx(1-sin^2 x)
= sinx - 2sin^3 x + 2sinx -2sin^3 x
= 3sinx -4sin^3 x