Answer
limit does not exist.
Work Step by Step
$\lim\limits_{x\to \pi^-}cotx$
$=cot\pi$
$=-\infty$
$\lim\limits_{x \to \pi^+} cotx
=cot\pi=\infty$
Since, right hand limit is not equal to the left hand limit,
$\lim\limits_{x \to \pi} cotx$ does not exist.
