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

we know 
$$a = b \cos C + c \cos B$$
$$b= a \cos C + c \cos A$$ 
$$c= b \cos A + a \cos B$$ 
adding together we get 
$$(a+b) \cos C + (b+c) \cos A + (c+a) \cos B =a +b+c $$ 
