Question

State true or false.

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

• A. True
• B. False

Answer 1

The correct option is A True

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

$=\sqrt{\frac{1+\sin A}{1-\sin A}}\times \sqrt{\frac{1-\sin A}{1-\sin A}}$

$=\sqrt{\frac{1-{\sin }^{2}A}{{(1-\sin A)}^2}}$

$=\sqrt{\frac{{\cos }^{2}A}{{(1-\sin A)}^2}}$

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

Hence the given statement is true.