Question

Упростите выражение

Answer 1

$frac{Sin4alpha}{1+Cos4alpha}*frac{Cos2alpha}{1+Cos2alpha } =frac{2Sin2alpha Cos2alpha}{2Cos^{2}2alpha}*frac{Cos2alpha}{2Cos^{2}alpha} =frac{Sin2alpha}{Cos^{2}alpha}=frac{2Sinalpha Cosalpha}{Cos^{2}alpha}=frac{2Sinalpha }{Cosalpha}=2tgalpha$

Answer 2

(sin4α/(1+cos4α))*(cos2α/1+cos2α)=(2sin2α*cos2α/2cos²2α)*(cos2α/2cos²α)=

sin2α/(2cos²α)=2sinα*cosα/(2cos²α)=sinα/cosα=tgα