Question

Prove the identity(Pre-Calc/Math 4):
Sin4x=(4sin(x)cos(x))(2cos^2(x)-1)

Answer 1

Hint:
\[
\sin(4x)=\sin(2\times 2x)
\]

Answer 2

\[\sin 2a=2\sin a \cos a\]
\[\cos 2a=\cos ^2a-\sin ^2a=\cos ^2a-(1-\cos ^2a)=2\cos ^2a-1\]