Question

Доказать: tg$alpha$+ctg$alpha$=$frac{2}{sin2 alpha }$

Answer 1

$tg alpha+ctg alpha =frac{2}{sin2 alpha }\frac{sin alpha }{cosalpha}+frac{cosalpha}{sinalpha}=frac{2}{sin2alpha}\frac{sin^2 alpha+cos^2 alpha }{sin alpha*cos alpha }=frac{2}{sin2 alpha }\frac{2}{sin2 alpha }=frac{2}{sin2 alpha }$
Примечание:
$sin^2 alpha +cos^2 alpha =1\sin alpha cos alpha =frac{sin2 alpha }{2}$