# Provet that? : cos(-x) -= cosx

Oct 25, 2016

This is a proof

#### Explanation:

We use the sum of angles formula:
$\cos \left(A \pm B\right) \equiv \cos A \cos B \pm \sin A \sin B$

Put $A = 0$ and $B = - x$ to get
$\cos \left(0 - x\right) \equiv \cos 0 \cos x - \sin 0 \sin x$

And we know that $\sin 0 = 0$ and $\cos 0 = 1$ so:
$\cos \left(- x\right) \equiv \left(1\right) \cos x - 0$
$\therefore \cos \left(- x\right) \equiv \cos x$ QED