The number of solutions of the equation x+2tanx=(π)/2 in the interval 0, 2π is

Q37 / 90 · JEE Main 2021 (17 Mar Shift 2) · Mathematics

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

We have $x + 2 \tan x = \frac{π}{2}$

$\Rightarrow 2 \tan x = \frac{π}{2} - x$

$\Rightarrow \tan x = - \frac{1}{2} x + \frac{π}{4}$

The graph of the two functions is given as

It is clear from the graph that the number of solutions of the given equation is $3 .$

Hence, the correct answer is option: 'A'.