Question

(tg(a-b)-tga+tgb)/(tg(a-b)*tgb)

Answer 1

$frac{tg(alpha-beta) +tgbeta-tgalpha }{tg(alpha -beta )cdot tgbeta} =frac{frac{tgalpha -tgbeta }{1+tgalpha cdot tgbeta } +tgbeta-tgalpha }{frac{(tgalpha -tgbeta)cdot tgbeta }{1+tgalpha cdot tgbeta } }=frac{tgalpha-tgbeta +tgbeta +tgalphacdot tg^2beta-tgalpha-tg^2alphacdot tgbeta }{(tgalpha-tgbeta)cdot tgbeta } =$

$=frac{tgalphacdot tg^2beta-tg^2alphacdot tgbeta}{(tgalpha-tgbeta)cdot tgbeta}=frac{-tgalphacdot tgbeta cdot(tgalpha -tgbeta) }{(tgalpha-tgbeta)cdottgbeta } = -tgalpha$