Question

Докажите тождество
tgA+ctgB/
ctgA+tgB
= tgA*ctgB

Answer 1

$frac{tgalpha+ctgbeta}{ctgalpha+tgbeta}=frac{frac{sinalpha}{cosalpha}+frac{cosbeta}{sinbeta}}{frac{cosalpha}{sinalpha}+frac{sinbeta}{cosbeta}}=frac{frac{sinalpha sinbeta+cosbeta cosalpha}{cosalpha sinbeta}}{frac{cosalpha cosbeta+sinbeta sinalpha}{sinalpha cosbeta}}=frac{frac{1}{cosalpha sinbeta}}{frac{1}{sinalpha cosbeta}}=frac{sinalpha cosbeta}{cosalpha sinbeta}=tgalpha ctgbeta$