QPaperGen

\begin{align*}
\text{LHS}&=\cos\left( \frac{3\pi}{2} + x \right)\cos(2\pi + x)\left[ \cot\left( \frac{3\pi}{2} - x \right) + \cot(2\pi + x) \right]\\ &= \sin x \cos x \left[ \tan x + \cot x \right] \\
&= \sin x \cos x \left( \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} \right) \\
&= \sin x \cos x \cdot \frac{\sin^2 x + \cos^2 x}{\sin x \cos x} \\
&= \frac{\sin^2 x + \cos^2 x}{1} = 1 = \text{RHS} \qquad \textbf{Hence proved.}
\end{align*}