Differentiate w . r . t x $\tan^{-1}\bigg[\large\frac{1-\cos x}{sin x}\bigg]; -\pi < x < \pi$

Question

$(A)\; \frac{dy}{dx} = \frac{-1}{2}$
$(B)\; \frac{dy}{dx} = \frac{1}{2}$
$(C)\; \frac{dy}{dx} = \frac{1}{4} $
$(D)\; \frac{dy}{dx} = \frac{-1}{4}$