The equation  $\tan \left|x\right|=\tan x,x\in [-2\pi ,2\pi ]$

If  $x\in [-2\pi ,0]$ then the equation is $\tan \left|x\right|=\tan x$ 
Which is satisfied by all x in  $[-2\pi ,0]$ 
Except  $\frac{3\pi }{2},\frac{\pi }{2} \Rightarrow \left(c\right)$  is true and (a), (b) are false.
If  $x\in (\frac{5\pi }{2},2\pi )$ then,  $\left|x\right|\in (2\pi ,\frac{5\pi }{2})$

$\Rightarrow \tan \left|x\right|>0$, but  $\tan x<0\Rightarrow \left(d\right)$  is false