Question

помогите с алгеброй срочно нужно

Answer 1

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

Второй способ :

$\frac{Sin\alpha }{1+Cos\alpha}+\frac{1+Cos\alpha}{Sin\alpha}=\frac{2Sin\frac{\alpha }{2}Cos\frac{\alpha }{2}}{2Cos^{2}\frac{\alpha} {2}} +\frac{2Cos^{2}\frac{\alpha}{2}}{2Sin\frac{\alpha} {2} Cos\frac{\alpha}{2}}=\frac{Sin\frac{\alpha }{2}}{Cos\frac{\alpha }{2}}+\frac{Cos\frac{\alpha }{2} }{Sin\frac{\alpha}{2} }=\frac{Sin^{2}\frac{\alpha }{2}+Cos^{2}\frac{\alpha}{2}}{Sin\frac{\alpha }{2}Cos\frac{\alpha }{2}}=\frac{1}{\frac{1}{2}Sin\alpha}=\frac{2}{Sin\alpha}$