The number of solutions

Question:

The number of solutions of the equation $x+2 \tan x=\frac{\pi}{2}$ in the interval $[0,2 \pi]$ is :

  1. 3

  2. 4

  3. 2

  4. 5


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'.

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