Si $y = \cot^{-1} \left[ \frac{\sqrt{1+\sin x} + \sqrt{1-\sin x}}{\sqrt{1+\sin x} - \sqrt{1-\sin x}} \right]$ para $0 < x < \pi/2$, entonces $\frac{dy}{dx} =$

a. $\frac{1}{2}$
b. $\frac{2}{3}$
c. $3$
d. $1$