# $\sin x+\sin y+\sin z=4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}$ [duplicate]

If $$x+y+z=\pi$$ how to prove that $$\sin x+\sin y+\sin z=4\cos\frac{x}{2}\cos\frac{y}{2}\cos\frac{z}{2}$$?

I got that $$\sin x+\sin y+\sin z=2\sin\frac{x+y}{2}\cos\frac{x-y}{2}+\sin x\cos y+\sin y\cos x$$ and I don't know what to do next.