$\int (1- \cos x) cosec^2 x dx =f(x)+c=>f(x)=$

Question

$$\begin {array} {1 1} (1)\;\tan \frac{x}{2} & \quad (2)\;\cot \frac{x}{2} \\ (3)\;2 \tan \frac{x}{2} & \quad (4)\;\frac{1}{2} \tan \frac{x}{2} \end {array}$$