Question

Помогите пожалуйста! Любой как сможете! Номер 527! Упростите выражение! Какой сможете! Любой!

Answer 1

$1)1-\frac{1}{Cos^{2}(\pi -\alpha)}=1-\frac{1}{Cos^{2}\alpha} =1-(1+tg^{2}\alpha)=1-1-tg^{2}\alpha=-tg^{2}\alpha$

$2)\frac{1-Sin(\pi-\alpha)}{Cos(2\pi-\alpha)}+Ctg(\pi-\alpha)=\frac{1-Sin\alpha}{Cos\alpha }-Ctg\alpha=\frac{1-Sin\alpha }{Cos\alpha }-\frac{Cos\alpha }{Sin\alpha} =\frac{Sin\alpha-Sin^{2}\alpha -Cos^{2}\alpha}{Sin\alpha Cos\alpha}=\frac{Sin\alpha-1 }{Sin\alpha Cos\alpha}$

$3)Ctg^{2}(\pi-\alpha)*(Sin^{2}(\frac{\pi }{2}-\alpha)-1)=Ctg^{2}\alpha*(Cos^{2}\alpha-1) =\frac{Cos^{2}\alpha}{Sin^{2}\alpha}*(-Sin^{2}\alpha)=-Cos^{2}\alpha$

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