Question

Prove that: $\frac{b^2-c^2}{\cos B+\cos C}+\frac{c^2-a^2}{\cos C+\cos A}+\frac{a^2-b^2}{\cos A+\cos B}=0.$

Answer 1

$\frac{b^2-c^2}{\cos B+\cos C}$=$\frac{k^2({\sin }^{2}B-{\sin }^{2}C)}{\cos B+\cos C}$
$=-k^2\frac{({\cos }^{2}B-{\cos }^{2}C)}{\cos B+\cos C}$
$\therefore L.H.S=-k^2\sum (\cos B-\cos C)=0$.