LHS
\begin{equation*}
\begin{split}
& \sqrt{\dfrac{1 - \cos x}{1 + \cos x}} \quad {\color {blue} \frac{1 - \cos x}{1 - \cos x}}\\ \\\\
& \sqrt{\frac{(1 - \cos x)^2}{(1 + \cos x)(1 - \cos x)}} \quad {\color {blue} (a + b)(a - b) = a^2 - b^2}\\\\
& \sqrt{\frac{(1 - \cos x)^2}{1 - \cos^2 x}} \quad {\color {blue} 1 - \cos^2 x = \sin^2 x}\\\\
& \sqrt{\frac{(1 - \cos x)^2}{\sin^2 x}} \\\\
& \frac{1 - \cos x} {\sin x}\\\\
& \frac{1}{\sin x} - \frac {\cos x} {\sin x}\\\\
& \csc x - \cot x \ce{->} \textbf{RHS}
\end{split}
\end{equation*}
LHS = RHS
