TITLE: Prove $(1-\cos x)/\sin x = \tan x/2$
QUESTION [7 upvotes]: 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?

REPLY [14 votes]: 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 $CD/ED = sin (\phi/2)$