The set of points of discontinuity

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 $\left\{(2 n+1) \frac{\pi}{2}: n \in \mathbf{Z}\right\}$

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