[tex]\displaystyle\bf\\\Big(\frac{Sin\alpha }{1+Cos\alpha } +\frac{Sin\alpha }{1-Cos\alpha } \Big)\cdot\frac{1}{1+Ctg^{2} \alpha } =\\\\\\=\frac{Sin\alpha \cdot(1-Cos\alpha )+Sin\alpha \cdot(1+Cos\alpha )}{(1+Cos\alpha )(1-Cos\alpha )} \cdot\frac{1}{1+Ctg^{2} \alpha } =\\\\\\=\frac{Sin\alpha-Sin\alpha \cdot Cos\alpha +Sin\alpha+Sin\alpha \cdot Cos\alpha }{1^{2} -Cos^{2} \alpha } \cdot\frac{1}{1+Ctg^{2} \alpha } =[/tex]

[tex]\displaystyle\bf\\=\frac{2Sin\alpha }{Sin^{2} \alpha } \cdot\frac{1}{\frac{1}{Sin^{2}\alpha } } =\frac{2}{Sin\alpha } \cdot Sin^{2} \alpha =2Sin\alpha[/tex]