Question

выполните 2 задание пожалуйста​

Answer 1

$(Sin2\alpha+3Cos2\alpha)^{2}+(Cos2\alpha-3Sin2\alpha){^{2}=$

$=Sin^{2}2\alpha+6Sin2\alpha Cos2\alpha +9Cos^{2} 2\alpha+Cos^{2}2\alpha -6Sin2\alpha Cos2\alpha+9Sin^{2} 2\alpha=\\\\=10Sin^{2}2\alpha+10Cos^{2}2\alpha=10\underbrace{(Sin^{2}2\alpha+Cos^{2}2\alpha)}_{1}=\boxed{10}$

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

Тождество доказано