Sin a/ 1+cos a + sin a/ -cos a

[latex] \frac{sina}{1+cosa} + \frac{sina}{a-cosa} = \frac{2sin\frac{a}{2}\cdot cos\frac{a}{2}}{2cos^2\frac{a}{2}} + \frac{2sin\frac{a}{2}\cdot cos\frac{a}{2}}{2sin^2\frac{a}{2}} = \frac{sin\frac{a}{2}}{cos\frac{a}{2}} + \frac{cos\frac{a}{2}}{sin\frac{a}{2}} =\\\\= \frac{sin^2\frac{a}{2}+cos^2\frac{a}{2}}{sin\frac{a}{2}\cdot cos\frac{a}{2}} =\frac{1}{\frac{1}{2}sina}=\frac{2}{sina}\\\\ili\; \; \; \; \frac{sina}{1+cosa}+\frac{sina}{1-cosa}=tg\frac{a}{2}+ctg\frac{a}{2}=(\; \frac{2}{sina}\; )[/latex]