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 find \( \tan \frac{C}{2} \) in triangle \( ABC \) given \( \tan \frac{A}{2} = \frac{5}{6} \) and \( \tan \frac{B}{2} = \frac{20}{37} \), we can use the following relationship:

\[ \tan \frac{C}{2} = \frac{\tan \frac{A}{2} + \tan \frac{B}{2}}{1 - \tan \frac{A}{2} \tan \frac{B}{2}} \]

### Step-by-Step Solution:

...