Verified answer

[tex]\displaystyle\bf\\\frac{Cos\alpha }{Sin2\alpha } +\frac{Sin\alpha }{Cos2\alpha } \cdot\frac{Sin4\alpha }{Cos\alpha } =\\\\\\=\frac{Cos\alpha }{2Sin\alpha Cos\alpha } +\frac{Sin\alpha }{Cos2\alpha } \cdot\frac{2Sin2\alpha Cos2\alpha }{Cos\alpha } =\\\\\\=\frac{1}{2Sin\alpha } +Sin\alpha \cdot\frac{2Sin2\alpha }{Cos\alpha } =\frac{1}{2Sin\alpha } +Sin\alpha \cdot\frac{4Sin\alpha Cos\alpha }{Cos\alpha } =\\\\\\=\frac{1}{2Sin\alpha } +4Sin^{2} \alpha =\frac{1+8Sin^{3} \alpha }{2Sin\alpha }[/tex]