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

⇒c = k sin C

Similarly, b = k sin B

So, b - c = k(sin B - sin C)..(i)

Here we will consider RHS, so we get

Substituting equation (i) in the 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,

Hence proved