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In a triangle ABC, if sinAsin(B-C)=sinCs...

In a triangle ABC, if `sinAsin(B-C)=sinCsin(A-B),` then prove that `cotA ,cotB ,cotCa r einAdotPdot`

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To prove that \( \cot A, \cot B, \cot C \) are in Arithmetic Progression (AP) given the equation \( \sin A \sin (B - C) = \sin C \sin (A - B) \), we will follow these steps: ### Step 1: Start with the given equation We have: \[ \sin A \sin (B - C) = \sin C \sin (A - B) \] ...
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