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 тАУ sin C) + b (sin C тАУ sin A) + c (sin A тАУ sin B)
Substituting the values of a, b, c from sine rule inabove equation, we get
a (sin B тАУ sin C) + b (sin C тАУ sin A) + c (sin A тАУ sinB) = k sin A (sin B тАУ sin C) + k sin B (sin C тАУ sin A) + k sin C (sin A тАУ sin B)
= k sin A sin B тАУ k sin A sin C + k sin B sin C тАУ ksin B sin A + k sin C sin A тАУ k sin C sin B
Upon simplification, we get
= 0
= RHS
Hence proved.