In triangle ABC,(b + c)cos A + (c + a)cos B + | vedclass

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(C) Given expression: $E = (b + c)\cos A + (c + a)\cos B + (a + b)\cos C$Expanding the terms: $E = b\cos A + c\cos A + c\cos B + a\cos B + a\cos C + b

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$a + b + c$

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(C) Given expression: $E = (b + c)\cos A + (c + a)\cos B + (a + b)\cos C$Expanding the terms: $E = b\cos A + c\cos A + c\cos B + a\cos B + a\cos C + b\cos C$Rearranging the terms: $E = (b\cos C + c\cos B) + (c\cos A + a\cos C) + (a\cos B + b\cos A)$Using the projection rule: $a = b\cos C + c\cos B$,$b = a\cos C + c\cos A$,and $c = a\cos B + b\cos A$Substituting these into the expression: $E = a + b + c$Therefore,the correct option is $C$.

In triangle $ABC$,$(b + c)\cos A + (c + a)\cos B + (a + b)\cos C = $

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