$\sqrt{\dfrac{\sec A + 1}{\sec A - 1}} = ?$

Multiply numerator and denominator inside the root by $(\sec A+1)$ (or use $\sec A=1/\cos A$); the expression simplifies to ${\displaystyle \frac{1+\cos A}{\sin A}}=\cot$. Since for the relevant range, the positive root gives option (a).