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.