Simplifying $\cos(x-360^\circ)$

Question

If $\cos(360^\circ + x)$ simplifies to $\cos x$, then how do I simplify $\cos(x - 360^\circ)$?

I have tried different online checks, and I cannot find a definitive answer.

Answer 1

Since $\cos$ is periodic with period $2\pi=360°$, $\forall k\in \mathbb{Z}$

$$\cos (x\pm k\cdot360°)=\cos x$$

Answer 2

Since you know $$\cos (360^\circ+x)=\cos(x)$$

Then,

$$\cos (x-360^\circ)= \cos (360^\circ+x-360^\circ)=\cos(x)$$