In a \( \triangle A B C \), if \( a, b \) and \( c \) are in A.P., prove that \( \cos A \cdot \c...

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In a \( \triangle A B C \), if \( a, b \) and \( c \) are in A.P., prove that \( \cos A \cdot \cot \frac{A}{2}, \cos B . \cot \frac{B}{2} \), and \( \cos C . \cot \frac{C}{2} \) are in A.P.
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