Question

$\sqrt{\frac{1+\sin A}{1-\sin A}}$ is equal to :

• A. $\frac{\cot A}{\sin A+\cos A}$
• B. $\frac{\cot A}{\text{cosec}A-1}$
• C. $\frac{\cot A}{\sec A-1}$
• D. $\frac{\cot A}{\tan A-1}$

Answer 1

The correct option is B $\frac{\cot A}{\text{cosec}A-1}$

The value of $\sqrt{\frac{1+\sin A}{1-\sin A}}$ is

$=\sqrt{\frac{1+\sin A}{1-\sin A}}\times \sqrt{\frac{1+\sin A}{1+\sin A}}$
$=\frac{1+\sin A}{\cos A}$
$=\frac{1+\sin A}{\cos A}\times \frac{\cos A}{\cos A}=\frac{\cos A(1+\sin A)}{{\cos }^{2}A}$
$=\frac{\cos A(1+\sin A)}{(1+\sin A)(1-\sin A)}=\frac{\cos A}{1-\sin A}$
$=\frac{\frac{\cos A}{\sin A}}{\frac{1-\sin A}{\sin A}}=\frac{\cot A}{\text{cosec}A-1}$