Question

Упростите выражение

Answer 1

$\frac{Sin4\alpha}{1+Cos4\alpha}*\frac{Cos2\alpha}{1+Cos2\alpha } =\frac{2Sin2\alpha Cos2\alpha}{2Cos^{2}2\alpha}*\frac{Cos2\alpha}{2Cos^{2}\alpha} =\frac{Sin2\alpha}{Cos^{2}\alpha}=\frac{2Sin\alpha Cos\alpha}{Cos^{2}\alpha}=\frac{2Sin\alpha }{Cos\alpha}=2tg\alpha$

Answer 2

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

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