Question

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

Answer 1

$\frac{tg(\alpha-\beta) +tg\beta-tg\alpha }{tg(\alpha -\beta )\cdot tg\beta} =\frac{\frac{tg\alpha -tg\beta }{1+tg\alpha \cdot tg\beta } +tg\beta-tg\alpha }{\frac{(tg\alpha -tg\beta)\cdot tg\beta }{1+tg\alpha \cdot tg\beta } }=\frac{tg\alpha-tg\beta +tg\beta +tg\alpha\cdot tg^2\beta-tg\alpha-tg^2\alpha\cdot tg\beta }{(tg\alpha-tg\beta)\cdot tg\beta } =$

$=\frac{tg\alpha\cdot tg^2\beta-tg^2\alpha\cdot tg\beta}{(tg\alpha-tg\beta)\cdot tg\beta}=\frac{-tg\alpha\cdot tg\beta \cdot(tg\alpha -tg\beta) }{(tg\alpha-tg\beta)\cdottg\beta } = -tg\alpha$