Mathematics - Properties of Triangle Question with Solution | TestHub

Expand cos(B-C)=cos B cos C+sin B sin C and cyclic. The sin products contribute 3abc/($4R^2$). For the cosine products, cos B cos C + cos C cos A + cos A cos B weighted by a,b,c reduces to c cos C + c[cos A cos B - cos(A+B)] after using a cos B+b cos A=c , a cos C+c cos A=b , and cos(A+B)=-cos C . The bracket equals sin A sin B, giving c sin A sin B=abc/($4R^2$) . Thus the total is abc/$R^2$.