reqired help solving $\cos(x)=-\cos(y)$ If I have $\cos(x)=-\cos(x+\alpha)$,   
can I solve it by doing
 $x=-(x+\alpha+2\pi)$ and $x=-(-(x+\alpha+2\pi))$?   
It's probably a stupid question but I'm really confused.

HINT: $$\cos(x)+\cos(y)=2\cos\left(\frac{x-y}{2}\right)\cos\left(\frac{x+y}{2}\right)$$
