Question : The value of $\frac{\sin A}{1+\cos A}+\frac{\sin A}{1-\cos A}$ is $(0°<A<90°)$:
Option 1: $2\operatorname{cosec}A$
Option 2: $2 \sec A$
Option 3: $2 \sin A$
Option 4: $2 \cos A$
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Correct Answer: $2\operatorname{cosec}A$
Solution :
Given: $\frac{\sin A}{1+ \cos A}+\frac{\sin A}{1- \cos A}$
= $\frac{\sin A(1–\cos A)+\sin A (1+\cos A)}{(1+ \cos A)(1- \cos A)}$
= $\frac{\sin A–\sin A \cos A+\sin A+\sin A \cos A}{(1- \cos^{2} A)}$
= $\frac{2\sin A}{\sin^{2}A}$
= $\frac{2}{\sin A}$
= $2 \operatorname{cosec}A$
Hence, the correct answer is $2 \operatorname{cosec}A$.
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