In `DeltaABC,(a+b+c)(tanA/2+tanB/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 use the half-angle formulas for tangent and properties of triangles. Let's break this down step by step.

### Step 1: Understand the Variables
In triangle \(ABC\):
- Let \(a\), \(b\), and \(c\) be the lengths of the sides opposite to angles \(A\), \(B\), and \(C\) respectively.
- The semi-perimeter \(S\) is given by:
\[
S = \frac{a + b + c}{2}
...