Question -
Answer -
By using the sine rule we know,
a = k sin A, b = k sin B, c = k sin C
Let us consider LHS:
a (sin B – sin C) + b (sin C – sin A) + c (sin A – sin B)
Substituting the values of a, b, c from sine rule inabove equation, we get
a (sin B – sin C) + b (sin C – sin A) + c (sin A – sinB) = k sin A (sin B – sin C) + k sin B (sin C – sin A) + k sin C (sin A – sin B)
= k sin A sin B – k sin A sin C + k sin B sin C – ksin B sin A + k sin C sin A – k sin C sin B
Upon simplification, we get
= 0
= RHS
Hence proved.