Question

The number of value(s) of $x\in [0,4\pi ]$ for which $\tan x=\sqrt{3}$ is

Answer 1

$\tan x=\sqrt{3}\Rightarrow \tan x=\tan \frac{\pi }{3}\Rightarrow x=n\pi +\frac{\pi }{3},n\in Z\Rightarrow x=\frac{\pi }{3},\frac{4\pi }{3},\frac{7\pi }{3},\frac{10\pi }{3}(\because x\in [0,4\pi \left]\right)$

Hence, the number of solutions of the equation is $4$.