If $x-a \bigg \{\cos \theta+ \log \tan \bigg(\large\frac{\theta}{2}\bigg)\bigg\}$ and $y= a \sin \theta$ then $\large\frac{dy}{dx}=$

Question

$$\begin {array} {1 1} (1)\;\cot \theta & \quad (2)\;\tan \theta \\ (3)\;\sin \theta & \quad (4)\;\cos \theta \end {array}$$