Question

Помогите упростить срочно!

Answer 1

$Sin2alpha +Cos2alpha *Ctgalpha =2Sinalpha Cosalpha +(Cos^{2}alpha -Sin^{2}alpha )*frac{Cosalpha}{Sinalpha}=2Sinalpha Cosalpha +frac{Cos^{3}alpha}{Sinalpha}-frac{Sin^{2}alpha*Cosalpha}{Sinalpha} =2Sinalpha Cosalpha+frac{Cos^{3}alpha}{Sinalpha} -Sinalpha Cosalpha=Sinalpha Cosalpha +frac{Cos^{3}alpha}{Sinalpha}=frac{Sin^{2}alpha Cosalpha+Cos^{3}alpha}{Sinalpha}=frac{Cosalpha(Sin^{2}alpha+Cos^{2}alpha)}{Sinalpha}=frac{Cosalpha}{Sinalpha}=Ctgalpha$

$Ctg2alpha -tg2alpha =frac{1}{tg2alpha} -tg2alpha =frac{1-tg^{2}2alpha}{tg2alpha} =frac{1}{frac{1}{2}tg4alpha} =frac{2}{tg4alpha}$