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

The correct answer is Option (1) → $\{x = n\pi : n \in \mathbb{Z}\}$ ##

We know that, $f(x) = \cot x$ is continuous in $R - \{x = n\pi \in \mathbb{Z}\}$.

Since, $f(x) = \cot x = \frac{\cos x}{\sin x} \quad [∵\sin x = 0 \text{ at } x = n\pi, n \in \mathbb{Z}]$

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