Answer
See the full explanation below.
Work Step by Step
Let us consider the left side of the given expression:
$\tan \left( 2\pi -x \right)$
By using the identity of trigonometry, $\tan \,\left( \alpha -\beta \right)=\frac{\tan \,\alpha -\tan \,\beta }{1+\tan \,\alpha \tan \,\beta }$, the above expression can be further simplified as:
$\begin{align}
& \tan \left( 2\pi -x \right)=\frac{\tan \,2\pi -\tan \,x}{1+\tan \,2\pi \tan \,x} \\
& =\frac{0-\tan \,x}{1+0\times \tan \,x} \\
& =\frac{-\tan \,x}{1} \\
& =-\tan \,x
\end{align}$
Hence, the the left side of the provided expression is equal to the right side, which is $\tan \left( 2\pi -x \right)=-\tan \,x$.
