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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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`ab^(2) cos A + ba^(2) cos B + ac^(2) cos A + ca^(2) cos C + bc^(2) cos B + b^(2) c cos C`
`= ab(b cos A + a cos B) + ac (c cos A + a cos C) + bc (c cos B + b cos C)`
`= abc + abc + abc = 3abc`
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