Question

Помоги упростить тригонометрические выражения

Answer 1

$2)frac{Sin(pi+alpha)Cos(pi-alpha)}{Ctg(frac{3pi }{2}-alpha)} =frac{-Sinalpha*(-Cosalpha)}{tgalpha}=frac{Sinalpha*Cosalpha*Cosalpha}{Sinalpha}=Cos^{2}alpha$

$3)frac{Sin^{4}alpha-Cos^{4}alpha}{Sinalpha*Cosalpha} =frac{(Sin^{2}alpha-Cos^{2}alpha)(Sin^{2}alpha+Cos^{2}alpha)}{Sinalpha*Cosalpha}=frac{-Cos2alpha*1 }{frac{1}{2}*(2Sinalpha Cosalpha)}=frac{-2Cos2alpha }{Sin2alpha}=-2Ctg2alpha$