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Prove that a(b^(2) + c^(2)) cos A + b(c^...

Prove that `a(b^(2) + c^(2)) cos A + b(c^(2) + a^(2)) cos B + c(a^(2) + b^(2)) cos C = 3abc`

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To prove the equation \( a(b^2 + c^2) \cos A + b(c^2 + a^2) \cos B + c(a^2 + b^2) \cos C = 3abc \), we will use the projection formulas and properties of triangles. ### Step-by-Step Solution: 1. **Start with the projection formulas**: We know from the projection formulas in a triangle: \[ a = b \cos C + c \cos B ...
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