Given, y sin ϕ = x sin (2θ + ϕ)

Adding 1 both sides:

Now,

Adding 1 both sides:

Dividing equation (i) by equation (ii):

{sin (-A) = -sin A & cos (-A) = cos A}

⇒ (x + y) cot (θ + ϕ) = (y -x) cot θ

Hence Proved