In a `DeltaABC`, if `tanA/2=5/6` and `tanB/2=20/37` then `tanC/2=`

Options

A. `4/5`
B. `3/5`
C. `2/5`
D. none of these

Explanation

To solve the problem, we need to find the value of \( \tan \frac{C}{2} \) given \( \tan \frac{A}{2} = \frac{5}{6} \) and \( \tan \frac{B}{2} = \frac{20}{37} \). We will use the formula that relates the tangents of half-angles in a triangle.

### Step-by-Step Solution:

1. **Use the Half-Angle Formula**:
We know that:
\[
\tan \frac{A + B}{2} = \frac{\tan \frac{A}{2} + \tan \frac{B}{2}}{1 - \tan \frac{A}{2} \tan \frac{B}{2}}
...