Let a, b, c be the sides of any triangle ABC. Then by applying the sine rule, we get

⇒ a = k sin A, b = k sin B, c = k sin C

Here we will consider LHS, so we get

Substituting corresponding values from sine rule in the above equation, we get

Canceling the like terms, we get

But sin(A - B) = sin A cos B – cos A sin B, so the above equation becomes

Cancelling the like terms, we get,

LHS = 0 = RHS

Hence proved