The number of solutions of the equation x + 2 tan x = π 2 in the interval 0 ,   2 π is

We have $x+2\tan x=\frac{\pi }{2}$

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

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

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$3.$