Answer :

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


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