Solving Trig Identities: From \sqrt{2+2cosx} to 2cos(x/2)

[Jenkz]

Homework Statement

How to get from

$$\sqrt{2+2cosx}$$
to

2cos(x/2)

The Attempt at a Solution

I'm pretty much stuck on this.
I can only see that is simplifies by taking out the common factor 2, which isn't correct.

 

[rock.freak667]

Well id cos2x=2cos²x-1, then cosx=2cos²(x/2)-1

 

[Jenkz]

Yup, thanks!