x sin3 θ + ycos3 θ = sin θ cos θ ....(i) and x sin θ = ycos θ...(ii) Equation (i) may be written as x sin θ. sin2 θ + ycos3 θ = sin θ cos θ ⇒ ycos θ sin2 θ + ycos3 θ = sin θ cos θ ⇒ ycos θ (sin2 θ + cos2 θ) = sin θ cos θ ⇒ ycos θ = sin θ cos θ ∴ y = sin θ ...(iii) Putting the value of y from (iii) in (ii), we get x sin θ = sin t .cos θ ⇒ x = cos θ ...(iv) Squaring (iii) and (iv) and adding , we get x2+y2 = cos2 θ + sin2 θ = 1