reqired help solving $\cos(x)=-\cos(y)$

Question

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.

user id:33337 231k · Accepted Answer

Hint:

$\cos(u+\pi)=-\cos u$

and

$\cos x=\cos A\implies x=2m\pi\pm A$

Where $m$ is any integer

user id:175066 82k · Accepted Answer

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

2 Answers 2