Trigonometric substitution Been out of touch with trigonometry for some time now. Need help proving this expression.
$$\sin^{2}\left(\frac{x}{2}\right) = \frac{1}{2}(1-\cos\left(x\right))$$
Any help will be appreciated. Thanks.

Hint: 1) $\cos(2a)=\cos(a+a)=2\cos^2(a)-1=1-2\sin^2(a)$ (using $\sin^2(a)+\cos^2(a)=1$). Now use the result with $a=x/2$.
