`" If "y=cot^(-1)[(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx))](0ltxltpi//2)," then "(dy)/(dx)=`

Options

A. `(1)/(2)`
B. `(2)/(3)`
C. 3
D. 1

Explanation

To solve the problem step by step, we start with the given function:

**Step 1: Define the function**
Let
\[ y = \cot^{-1} \left( \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} \right) \]

**Step 2: Rationalize the expression**
We will rationalize the denominator:
...