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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.

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closed as off-topic by user21820, Lord Shark the Unknown, Shailesh, José Carlos Santos, Parcly Taxel Oct 23 '18 at 10:36

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

Then,

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

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

$$\cos (x\pm k\cdot360°)=\cos x$$

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