Question

Prove identity
tan((a+b)/2) = (sin(a)+sin(b))/(cos(a)+cos(b))

Answer 1

Sorry, bad connection...

I found this one on wiki: http://en.wikipedia.org/wiki/Tangent_half-angle_formula
WolframAlpha agrees: http://www.wolframalpha.com/input/?i=tan%28%28a%2Bb%29%2F2%29+%3D+%28sin%28a%29%2Bsin%28b%29%29%2F%28cos%28a%29%2Bcos%28b%29%29&dataset=

Does anyone have a proof?

Answer 2

you may proceed from RHS to LHS :
use them :

cos u + cos v = 2 cos(1/2 (u+v)) cos(1/2 (u−v))
sin u + sin v = 2 sin(1/2 (u+v)) cos(1/2 (u−v))

Answer 3

this maybe should help