Question

In any $△ABC$, prove the following :
$(b+c)\cos A+(c+a)\cos B+(a+b)\cos C=a+b+c$.

Answer 1

Re-writing the lefhand side, we get
$L.H.S=(b\cos C+c\cos B)+(c\cos A+a\cos C)+(a\cos B+b\cos A)=a+b+c$.