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If A+B+C=pi/2,prove that: sin2A-sin2B+...

If A+B+C=`pi/2`,prove that:
`sin2A-sin2B+sin2C=4sinAcosBsinC`

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AI Generated Solution

To prove the equation \( \sin 2A - \sin 2B + \sin 2C = 4 \sin A \cos B \sin C \) given that \( A + B + C = \frac{\pi}{2} \), we can follow these steps: ### Step 1: Rewrite \( C \) Since \( A + B + C = \frac{\pi}{2} \), we can express \( C \) in terms of \( A \) and \( B \): \[ C = \frac{\pi}{2} - (A + B) \] ...
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