The value of $$\frac{{{\text{sin A}}}}{{1 + \cos {\text{ A}}}}$$   + $$\frac{{{\text{sin A}}}}{{1 - \cos {\text{ A}}}}$$   is $$\left( {{0^ \circ } < {\text{A}} < {{90}^ \circ }} \right)$$

Solution(By Examveda Team)

$$\eqalign{ & \frac{{{\text{sin A}}}}{{1 + \cos {\text{ A}}}}{\text{ + }}\frac{{{\text{sin A}}}}{{1 - \cos {\text{ A}}}} \cr & \Rightarrow \frac{{{\text{sin A}}\left( {1 - \cos {\text{ A}}} \right) + {\text{sin A}}\left( {1 + \cos {\text{ A}}} \right)}}{{\left( {1 + \cos {\text{ A}}} \right)\left( {1 - \cos {\text{ A}}} \right)}} \cr & \Rightarrow \frac{{{\text{sin A}} - {\text{sin A}}{\text{.cosA}} + {\text{sin A}} + {\text{sin A}}{\text{.cosA}}}}{{{\text{1}} - {\text{co}}{{\text{s}}^2}{\text{A}}}} \cr & \Rightarrow \frac{{2{\text{sin A}}}}{{{{\sin }^2}{\text{A}}}} \cr & \Rightarrow 2{\text{ cosec A}} \cr} $$