Question

In any traingle ABC, $\sum a\sin (B-C)$ is equal to

Answer 1

$\sum a\sin (B-C)=\sum k\sin A\sin (B-C)$ (u\sin g \sin e formulae)

$=k\sum \sin (B+C)\sin (B-C)$

$=k\sum ({\sin }^{2}B-{\sin }^{2}C)$

$=k({\sin }^{2}B-{\sin }^{2}C+{\sin }^{2}C-{\sin }^{2}A+{\sin }^{2}A-{\sin }^{2}B)=0$