Prove that : c/(a-b) = [tan(A/2)+tan(B/2)]/[tan(A/2)-tan(B/2)]

Question

Prove that :

\(\frac{c}{a-b}=\frac{tan\frac{A}{2}+tan\frac{B}{2}}{tan\frac{A}{2}-tan\frac{B}{2}}\)

Answer 1

LHS = \(\frac{c}{a\,-\,b}=\frac{k\,sin\,C}{k\,sin\,A\,-k\,sin\,B}\)

 

Divide by cos\(\frac{A}{2}\).cos \(\frac{B}{2}\)

= LHS = RHS