[tex]\displaystyle \\ \texttt{Folosim formula:} \\ \\
\text{ctg} \frac{x}{2} = \frac{\sin x}{1-\cos x} = \frac{1+\cos x}{\sin x} \\ \\ \\
\Longrightarrow ~~~\frac{\sin x}{1-\cos x} - \frac{1+\cos x}{\sin x} = \text{ctg} \frac{x}{2} - \text{ctg} \frac{x}{2} = \boxed{0}[/tex]
