Question

Prove that ——
1-cos theta/sin theta=tan theta/2

Answer 1

let theta=©
so we need to prove that
1-cos©/sin©=tan©/2
RHS= TAN©/2
sin©/cos©/2
sin©/2cos©

Answer 2

First use the identities,

$1-\cos \theta = 2\sin^2(\frac{\theta}{2}) \\ \sin \theta =2\sin(\frac{\theta}{2}) \cos(\frac{\theta}{2})$

So,

$LHS=\frac{1-\cos \theta }{\sin \theta}\\ LHS=\frac{2\sin^2(\frac{\theta}{2}) }{2\sin(\frac{\theta}{2}) \cos(\frac{\theta}{2}) }\\ LHS=\frac{\sin(\frac{\theta}{2}) }{ \cos(\frac{\theta}{2}) }\\ LHS=\tan(\frac{\theta}{2}) =RHS$

The proof is complete.