Question

Упростите выражения 10 класс. Очень нужна помощь

Answer 1

$1)Sin(\alpha-\beta)+2Sin\beta Cos\alpha=Sin\alpha Cos\beta-Sin\beta Cos\alpha+2Sin\beta Cos\alpha=Sin\alpha Cos\beta+Sin\beta Cos\alpha=Sin(\alpha+\beta)=Sin\pi=0$

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