Question

cot (x/2) = -1

Answer 1

\[\cot(\frac{x}{2})=-1\iff \tan(\frac{x}{2})=-1\] is a start

Answer 2

\[\cot \frac{x}{2} =-1\rightarrow \cot \frac{x}{2} =-\cot \frac{\pi}{4}\]
I.E. \[\cot \frac{x}{2} =\cot (\pi -\frac{\pi}{4}) \rightarrow \cot \frac{3\pi}{4}\]
\[\cot \frac{x}{2}=\cot \frac{3\pi}{4} \rightarrow \frac{x}{2}=\frac{3\pi}{4} \rightarrow x= \frac{3\pi}{2}\]