Question

The set of points of discontinuity of f(x) = tan x is ___________.

Answer 1

The given function is $f\left(x\right)=\tan x$.

$f\left(x\right)=\tan x=\frac{\sin x}{\cos x}$

The function f(x) is discontinuous when $\cos x=0$.

$\cos x=0$

$\Rightarrow x=\left(2n+1\right)\frac{\mathrm{\pi }}{2},n\in \mathbf{Z}$

Thus, the set of point of discontinuity of $f\left(x\right)=\tan x$ is $\left\{\left(2n+1\right)\frac{\mathrm{\pi }}{2}:n\in \mathbf{Z}\right\}$.


The set of points of discontinuity of f(x) = tan x is $\underline{\left\{\left(2n+1\right)\frac{\mathrm{\pi }}{2}:n\in \mathbf{Z}\right\}}$.