Question

Упростите выражение:$sin2alpha -sin 4alpha /cos2alpha +cos4alpha$

Answer 1

$displaystyle frac{sin2alpha-sin4alpha}{cos2alpha+cos4alpha}=frac{sin2alpha-2sin2alphacos2alpha}{cos2alpha+2cos^22alpha-1}=frac{sin2alpha(1-2cos2alpha)}{2cos^22alpha+cos2alpha-1}=\ \ \ =frac{sin2alpha(1-cos2alpha)}{(cos2alpha+1)(2cos2alpha-1)}=-frac{2sinalphacosalpha}{2cos^2alpha-1+1}=-frac{sinalpha}{cosalpha}=-{rm tg},alpha$