Trigonometry – How to Derive $ \cot(\theta/2)$ from $ \frac {\sin \theta} {1 – \cos \theta} $?

Question

According to wolfram alpha, $\dfrac {\sin \theta} {1 – \cos \theta} = \cot \left(\dfrac{\theta}{2} \right)$.

But how would you get to $\cot \left(\dfrac{\theta}{2} \right)$ if you're given $\dfrac {\sin \theta} {1 – \cos \theta}$?

Answer 1

Proof without words: $\displaystyle\cot(\theta/2)=\frac{\color{green}{\sin(\theta)}}{\color{red}{1-\cos(\theta)}}$

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