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sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=co...

`sin(n+1)xsin(n+2)x+cos(n+1)xcos(n+2)x=cosx`

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To prove that \( \sin((n+1)x) \sin((n+2)x) + \cos((n+1)x) \cos((n+2)x) = \cos(x) \), we will use the cosine addition formula. ### Step-by-Step Solution: 1. **Start with the Left-Hand Side (LHS)**: \[ \text{LHS} = \sin((n+1)x) \sin((n+2)x) + \cos((n+1)x) \cos((n+2)x) \] ...
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