<s>[INST] Prove $(1-\cos x)/\sin x = \tan x/2$ Using double angle and compound angles formulae prove,
$$
\frac{1-\cos x}{\sin x}     = \tan\frac{x}{2}
$$
Can someone please help me figure this question, I have no idea how to approach it?
 [/INST] $$
\cos x = \cos^2\frac{x}{2}-\sin^2\frac{x}{2} = 1-2\sin^2\frac{x}{2}
$$
and
$$
\sin x = 2\sin\frac{x}{2}\cos\frac{x}{2}
$$
so
$$
\frac{1-\cos x}{\sin x} = \frac{2\sin^2\frac{x}{2}}{2\sin\frac{x}{2}\cos\frac{x}{2}} = \frac{\sin\frac{x}{2}}{\cos\frac{x}{2}} = \tan\frac{x}{2}
$$
</s>