The function $f(x) = \cot x$ is discontinuous on the set

We know that, $f(x) = \cot x$ is continuous in $R - \{ n\pi :n \in Z\}$.
Since, $f(x) = \cot x = \frac{{\cos x}}{{\sin x}}$ $[{\rm{since}},\sin x = 0\,{\rm{at}}\,n\pi ,n \in Z]$

Hence, $f(x) = \cot x$ is discontinuous on the set $\{ x = n\pi :n \in Z\}$.