In `DeltaABC,(a+b+c)(tan(A/2)+tan (B/2))=`

Options

A. `2c cotC/2`
B. `2acotA/2`
C. `2bcotB/2`
D. `tanC/2`

Explanation

To solve the problem \( (a+b+c)(\tan(A/2) + \tan(B/2)) \) in triangle \( ABC \), we will follow these steps:

### Step-by-Step Solution:

1. **Identify the formulas for \( \tan(A/2) \) and \( \tan(B/2) \)**:
\[ \tan\left(\frac{A}{2}\right) = \frac{\Delta}{s(s-a)} \quad \text{and} \quad \tan\left(\frac{B}{2}\right) = \frac{\Delta}{s(s-b)} \]
...