Question

The number of real solutions of $\frac{\pi }{2}+{\cos }^{-1}\left(\cos x\right)=|\tan x|,0\le x\le 2\pi$ is ________.

Answer 1

$\begin{array}{c}\frac{\pi }{2}\to {\cos }^{-1}\left(\cos x\right)=\left(\tan x\right)\\ in\left(0,\frac{\pi }{2}\right)\to valueexist\\ in\left(\frac{\pi }{2},\pi \right)\to exist\\ in\left(\pi ,\frac{3\pi }{2}\right)\to valueexist\\ in\left(\frac{3\pi }{2},2\pi \right)\to valueexist\\ Total4solution.\end{array}$