Question:
The number of solutions of the equation $x+2 \tan x=\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :
Correct Option: 1
Solution:
$x+2 \tan x=\frac{\pi}{2}$
$\Rightarrow 2 \tan x=\frac{\pi}{2}-x$
$\Rightarrow \tan x=-\frac{1}{2} x+\frac{\pi}{4}$
Number of soluitons of the given eauation is '3'.