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

⇒a = k sin A

Similarly, b = k sin B

So, a - b = k(sin A - sin B)..(i)

So the given LHS becomes,

Substituting equation (i) in above equation, we get

But,

Substituting the above values in equation (ii), we get

Rearranging the above equation we get

But

So the above equation becomes,

But from sine rule,

So the above equation becomes,

Hence proved