trigonometry identity I have some problem with proving this identity: 

$$2\left(1+\cos\alpha \right)-\sin^2\alpha=4\cos^4\frac{\alpha}{2}$$

I tried to start from the right side rewritting it to $(2\cos^2(2\frac{\alpha}{4}))^2$ but it's not working.
Replacing $\sin^2(x)=1-\cos^2(x)$ gives
$$
\begin{align}
2(1+\cos(\alpha))-\sin^2(\alpha)
&amp;=1+2\cos(\alpha)+\cos^2(\alpha)\\[6pt]
&amp;=(1+\cos(\alpha))^2\\
&amp;=\left(2\cos^2\left(\frac\alpha2\right)\right)^2
\end{align}
$$
using the identity $\cos(\alpha)=2\cos^2\left(\frac\alpha2\right)-1$.
begin by writing sin a = 2sin a/2 cos a/2 in left side ,easy by factoring you will have the answer