Question

Помоги упростить тригонометрические выражения

Answer 1

$2)\frac{Sin(\pi+\alpha)Cos(\pi-\alpha)}{Ctg(\frac{3\pi }{2}-\alpha)} =\frac{-Sin\alpha*(-Cos\alpha)}{tg\alpha}=\frac{Sin\alpha*Cos\alpha*Cos\alpha}{Sin\alpha}=Cos^{2}\alpha$

$3)\frac{Sin^{4}\alpha-Cos^{4}\alpha}{Sin\alpha*Cos\alpha} =\frac{(Sin^{2}\alpha-Cos^{2}\alpha)(Sin^{2}\alpha+Cos^{2}\alpha)}{Sin\alpha*Cos\alpha}=\frac{-Cos2\alpha*1 }{\frac{1}{2}*(2Sin\alpha Cos\alpha)}=\frac{-2Cos2\alpha }{Sin2\alpha}=-2Ctg2\alpha$