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In DeltaABC, prove that: (b-c)^(2)cos^...

In `DeltaABC`, prove that:
`(b-c)^(2)cos^(2)A/2+(b+c)^(2)sin^(2)A/2=a^(2)`

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AI Generated Solution

To prove the equation \((b-c)^{2}\cos^{2}\left(\frac{A}{2}\right) + (b+c)^{2}\sin^{2}\left(\frac{A}{2}\right) = a^{2}\) in triangle \(ABC\), we will start from the left-hand side and manipulate it step by step. ### Step-by-Step Solution: 1. **Start with the Left-Hand Side (LHS)**: \[ LHS = (b-c)^{2}\cos^{2}\left(\frac{A}{2}\right) + (b+c)^{2}\sin^{2}\left(\frac{A}{2}\right) \] ...
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