Properties of the Real Cotangent Function

Theorem: Image of the Real Cotangent Function

The image of the real cotangent function is $(-\infty ;+\infty )$.

PROOF

TODO

Theorem: Periodicity of the Real Cotangent Function

The real cotangent function has a period of $\pi$. More generally,

$\cot (x+k\pi )=\cot (x)\forall k\in \mathbb{Z}$

PROOF

TODO