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Prove that: sin(A+2B)sinA-sinBsin(2A+B...

Prove that:
`sin(A+2B)sinA-sinBsin(2A+B)sinB=sin(A+B)sin(A-B)`

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To prove the identity \( \sin(A + 2B) \sin A - \sin B \sin(2A + B) = \sin(A + B) \sin(A - B) \), we will use trigonometric identities and properties. ### Step-by-Step Solution: 1. **Start with the Left-Hand Side (LHS)**: \[ \text{LHS} = \sin(A + 2B) \sin A - \sin B \sin(2A + B) \] ...
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