Question:
The set of points of discontinuity of f(x) = tan x is ___________.
Solution:
The given function is $f(x)=\tan x$
$f(x)=\tan x=\frac{\sin x}{\cos x}$
The function $f(x)$ is discontinuous when $\cos x=0$.
$\cos x=0$
$\Rightarrow x=(2 n+1) \frac{\pi}{2}, n \in \mathbf{Z}$
Thus, the set of point of discontinuity of $f(x)=\tan x$ is $\left\{(2 n+1) \frac{\pi}{2}: n \in \mathbf{Z}\right\}$.
The set of points of discontinuity of $f(x)=\tan x$ is $\left\{(2 n+1) \frac{\pi}{2}: n \in \mathbf{Z}\right\}$