Answer
$$\tan(2\pi-x)=-\tan x$$
Work Step by Step
$$X=\tan(2\pi-x)$$
According to tangent difference identity:
$$\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$$
Expand $X$:
$$X=\frac{\tan2\pi-\tan x}{1+\tan2\pi\tan x}$$
In the trigonometric circle, point $2\pi$ collides with point $0$. Therefore, $\tan2\pi=\tan0=0$.
$$X=\frac{0-\tan x}{1+0\times\tan x}$$
$$X=\frac{-\tan x}{1}$$
$$X=-\tan x$$
Overall,
$$\tan(2\pi-x)=-\tan x$$
