Question

If $\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A$ then $A$ lies in which of the following quadrants?

Answer 1

The term on the RHS is defined only for $1-\sin A\ne 0\Rightarrow A\ne (4n+1)\frac{\pi }{2}$, for $n$ being and integer.

Also, the domain of $\tan A$ is $-\frac{\pi }{2}<A<\frac{\pi }{2}$ and that of $\sec A$ is $0\le A\le \pi$, $A\ne \frac{\pi }{2}$.

Now, for the given question, option (B) is going to be correct.

As the quadrant of the ramaining options contains $\frac{\pi }{2}$.