tga + tgb = sina/cosa + sinb/cosb = (sina.cosb + sinb.cosa)/cosa.cosb =
sin(a+b)/cosa.cosb

[(sina+sinb)/(sina-sinb)].tg(ab/2) = [ 2sin(a+b)/2 . cos(a-b)/2 ] .tg(ab/2) / [2sin(a-b)/2 . cos(a+b)/2] =
= tg(a+b)/2 . cotg(a-b)/2 . tg(a.b)/2