Question

The value of $\frac{\sin A}{1+\cos A}+\frac{\sin A}{1-\cos A}$ is $(0^o<A<{90}^o)$:

• A. $2\csc A$
• B. $2\sec A$
• C. $2\sin A$
• D. $2\cos A$

Answer 1

The correct option is A $2\csc A$

$\frac{\sin A}{1+\cos A}+\frac{\sin A}{1-\cos A}$

$=\frac{\sin A(1-\cos A)+\sin A(1+\cos A)}{(1+\cos A)(1-\cos A)}$

$=\frac{\sin A-\sin A\cos A+\sin A+\sin A\cos A}{1-{\cos }^{2}A}$

$=\frac{2\sin A}{{\sin }^{2}A}$

$=\frac{2}{\sin A}$

$=2\csc A$

Hence the correct option is (A).