simplification of $\cos\left( \frac{1}{2}\arcsin (x)\right)$ I know this identity :Simplifying $\cos(\arcsin x)$? but how I can simplify 

$$\cos\left( \frac{1}{2}\arcsin (x)\right)$$

if you have any idea. It could also be a sinus instead of a cosinus. When I do it I loop on something...

Note that $$\cos(2t)=2\cos^2(t)-1$$ now set $t=\arcsin(x)/2$ resulting:
\begin{align}
\cos(\arcsin(x))=2\cos^2(\arcsin(x)/2)-1
\end{align}
You can take it from here, right?
