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?