In $\Delta ABC, (a+b+c) \bigg(\tan \large\frac{A}{2}$$+\tan \large\frac{B}{2}\bigg)$ is equal to

Question

$$\begin {array} {1 1} (a)\;2c \cot \frac{C}{2} & \quad (b)\;2a \cot \frac{A}{2} \\ (c)\;2b \cot \frac{B}{2} & \quad (d)\;\tan \frac{C}{2} \end {array}$$