The value of sin A1 + A + sin A1 - A is ( 0^ < A < 90^ )

Answer: Option A

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