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

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

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$a+b+c$

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(B) Given expression: $(b+c) \cos A + (c+a) \cos B + (a+b) \cos C$ Expand the terms: $(b \cos A + c \cos A) + (c \cos B + a \cos B) + (a \cos C + b \cos C)$ Rearrange the terms: $(b \cos A + a \cos B) + (c \cos A + a \cos C) + (c \cos B + b \cos C)$ Using the projection formula for a triangle: $c = a \cos B + b \cos A$ $b = a \cos C + c \cos A$ $a = b \cos C + c \cos B$ Substituting these into the rearranged expression: $= c + b + a = a + b + c$

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

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