Question

Помогите пожалуйста сделать​

Answer 1

$1)(Sin\alpha +Cos\alpha)^{2}+(Sin\alpha-Cos\alpha)^{2}=\\\\=Sin^{2}\alpha+2Sin\alpha Cos\alpha+Cos^{2} \alpha+Sin^{2}\alpha-2Sin\alpha Cos\alpha+Cos^{2} \alpha =\\\\=2Sin^{2}\alpha+2Cos^{2}\alpha=2\underbrace{(Sin^{2}\alpha+Cos^{2}\alpha)}_{1}=2*1=\boxed2\\\\\\2)\frac{1}{Sin\alpha }-Cos\alpha Ctg\alpha=\frac{1}{Sin\alpha }-Cos\alpha*\frac{Cos\alpha }{Sin\alpha} =\frac{1-Cos^{2}\alpha }{Sin\alpha}=\\\\=\frac{Sin^{2}\alpha}{Sin\alpha }=\boxed{Sin\alpha}$

$3)\frac{tg\alpha Ctg\alpha}{Cos^{2}\alpha}-tg^{2}\alpha=\frac{1}{Cos^{2}\alpha} -\frac{Sin^{2}\alpha}{Cos^{2}\alpha}=\frac{1-Sin^{2}\alpha }{Cos^{2}\alpha}=\frac{Cos^{2}\alpha }{Cos^{2}\alpha} =\boxed1$