Proof This a(cosB+cosC-1)+b(cosC+cosA-1)+c(cosA+cosB-1)=0 you can use sine rule and cos rule.
What the question doesn't mention is that ABC is a triangle.
I only used the cosine rule. I converted CosA, cosB and cos c for its cos rule equivant.
then I expanded each bracket.
then I collected terms with a common denominator and simplified the numerators.
then it all just fell out.