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

Hint - draw a diagram of a triangle and see if you can mark a segment of length $b\cos A$ on side $c$ to get a geometric intuition about what is going on here.
