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 show that \( \cos A, \cos B, \cos C \) are in arithmetic progression (AP) given that \( \tan \frac{A}{2}, \tan \frac{B}{2}, \tan \frac{C}{2} \) are in AP, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Given Condition**:
Since \( \tan \frac{A}{2}, \tan \frac{B}{2}, \tan \frac{C}{2} \) are in AP, we can express this as:
\[
\tan \frac{B}{2} - \tan \frac{A}{2} = \tan \frac{C}{2} - \tan \frac{B}{2}
...