If the cotangents of half the angles of a triangle are in A.P., then prove that the sides are in A.P.

Explanation

To prove that the sides of a triangle are in Arithmetic Progression (A.P.) if the cotangents of half the angles are in A.P., we will follow these steps:

### Step 1: Understand the Given Condition
We are given that \( \cot \frac{A}{2}, \cot \frac{B}{2}, \cot \frac{C}{2} \) are in A.P. This means:
\[ \cot \frac{B}{2} - \cot \frac{A}{2} = \cot \frac{C}{2} - \cot \frac{B}{2} \]

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