Question

The points of discontinuity of $\tan x$ are

• A. $n\pi ,n\in I$
• B. $2n\pi ,n\in I$
• C. $(2n+1)\frac{\pi }{2},n\in I$
• D. None of the above

Answer 1

The correct option is C $(2n+1)\frac{\pi }{2},n\in I$

Let $f\left(x\right)=\tan x$
The points of discontinuity of $f\left(x\right)$ are those points where $\tan x$ is infinite. This gives
$\tan x=\infty$
ie $\tan x=\tan \frac{\pi }{2}$
$x=(2n+1)\frac{\pi }{2},n\in I$