Trig multiple angle identity I have a quick problem that I can't solve. I know it's simple, but I can't seem to crack it. 
Determine whether the equation is an identity. Answer true or false. 
$$
\sin4\theta = \cos\theta(4\sin\theta-8\sin^3\theta)
$$
The answer is true. Any help would be appreciated. 

You may write
$$
\begin{align}
\sin4\theta
&=2\sin(2\theta)\cos(2\theta)\\\\
&=\cos \theta \:(4\sin\theta\cos(2\theta))\\\\
&=\cos \theta \:(4\sin\theta(\cos^2\theta-\sin^2 \theta))\\\\
&=\cos \theta \:(4\sin\theta(1-2\sin^2 \theta))\\\\
&=\cos \theta \:(4\sin\theta-8\sin^3 \theta)\\\\
\end{align}
$$ as announced.
