Trigonometry – How to Prove $(1-\cos x)/\sin x = \tan x/2$

Question

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?

Answer 1

Use geometry: $AO= 1$ It is strange that no one has mentioned this drawing yet.

P.S. Note that you can easily extract other trigonometric identites involving $\phi/2, 2\phi $ argument from this picture. For example to get $sin(\phi/2)$ use $ECD$ triangle and Pythagorean theorem to calculate $CD/ED = sin (\phi/2)$