In any triangle ABC,the value of a(b^2 + c^2) | vedclass

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(C) The given expression is $E = a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$. Expanding the terms,we get: $E = ab^2\cos A + ac^2\cos

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$3abc$

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(C) The given expression is $E = a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$. Expanding the terms,we get: $E = ab^2\cos A + ac^2\cos A + bc^2\cos B + ba^2\cos B + ca^2\cos C + cb^2\cos C$. Grouping the terms: $E = ab(b\cos A + a\cos B) + bc(c\cos B + b\cos C) + ca(a\cos C + c\cos A)$. Using the projection formula $c = b\cos A + a\cos B$,$a = c\cos B + b\cos C$,and $b = a\cos C + c\cos A$: $E = ab(c) + bc(a) + ca(b) = abc + abc + abc = 3abc$.

In any triangle $ABC$,the value of $a(b^2 + c^2)\cos A + b(c^2 + a^2)\cos B + c(a^2 + b^2)\cos C$ is

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