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Prove that a cos A + b cos B + c cos C =...

Prove that `a cos A + b cos B + c cos C = 4 R sin A sin B sin C.`

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To prove that \( a \cos A + b \cos B + c \cos C = 4R \sin A \sin B \sin C \), we will follow these steps: ### Step 1: Express sides in terms of angles and circumradius We know that the sides of the triangle can be expressed in terms of the circumradius \( R \) and the angles \( A, B, C \): \[ a = 2R \sin A, \quad b = 2R \sin B, \quad c = 2R \sin C \] ...
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