How would I prove the following identity?
$\sin x=2\sin\frac{x}{2}\cos\frac{x}{2}$
I know $\sin(a+b)=\sin a\cos b+\sin a \cos b.$
So I did
$\sin\frac{x}{2}\cos\frac{x}{2}+\cos\frac{x}{2}\sin\frac{x}{2}.$
But what technique would I have to use to continue the problem?