Calcular $\frac{dy}{dx}$ para $y = \tan^{-1} \left\{ \sqrt{\frac{1 + \cos x}{1 - \cos x}} \right\}$, donde $0 < x < \pi$.

1. [a.] $-1/2$
2. [b.] $0$
3. [c.] $1$
4. [d.] $-1$