For any ΔABC, prove that sin (B-C)/2 = (b-c)/2 cos a/2

Question

For any ΔABC, prove that sin \(\frac{B - C}{2} = \frac{b -c}{2}cos \frac{A}{2}\)

Answer 1

Let \(\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C} = k\)

RHS = \(\frac{b-a}{a} cos \frac{A}{2} = \frac{k sin B - k sin C}{k sin A} cos \frac{A}{2}\)