Question

Доказать тождество.
tg(a)+ctg(a)=2/sin2a

Answer 1

$tg alpha+ctgalpha=frac{sinalpha}{cosalpha}+frac{cosalpha}{sinalpha}=frac{sin^2alpha}{sinalpha cosalpha}+frac{cos^2alpha}{sinalpha cosalpha} = \ =frac{sin^2alpha+cos^2alpha}{sinalpha cosalpha}=frac{1}{frac{1}{2}cdot2sinalpha cosalpha}=frac{1}{frac{1}{2}sin2alpha}=frac{2}{sin2alpha}$