Question

Find the number of solutions of the equations;

$x+\tan x=\frac{\pi }{2}$ when $x\in [0,2\pi ]$

Answer 1

Let $f\left(x\right)=\tan x,g\left(x\right)=\pi /2-x$
From graph clearly both the curves intersect at three points in the given interval.
Hence there is three solution in $[0,2\pi ]$