In a ` /_\A B C ,` if `tanA/2,tanB/2,tanC/2"are in"AdotPdot,` then show that `cosA ,cosB ,cosC` are in `AdotPdot`

Explanation

To solve the problem, we need to show that if \( \tan \frac{A}{2}, \tan \frac{B}{2}, \tan \frac{C}{2} \) are in arithmetic progression (AP), then \( \cos A, \cos B, \cos C \) are also in AP.

### Step-by-Step Solution:

1. **Given Condition**:
We start with the fact that \( \tan \frac{A}{2}, \tan \frac{B}{2}, \tan \frac{C}{2} \) are in AP. This means:
\[
2 \tan \frac{B}{2} = \tan \frac{A}{2} + \tan \frac{C}{2}
...