If x sin^3Ø + y cos^3Ø = sin cos Ø and x sin Ø = y cos Ø, prove that
x^2 + y^2 = 1.​

1 thought on “If x sin^3Ø + y cos^3Ø = sin cos Ø and x sin Ø = y cos Ø, prove that<br />x^2 + y^2 = 1.​”

1. Answer:

   Step-by-step explanation:

   Given : x sin3 θ + y cos3 θ = sin θ cos θ

   ⇒ (x sin θ) sin2 θ + (y cos θ) cos2 θ = sin θ cos θ

   ⇒ (x sin θ) sin2 θ + (x sin θ) cos2 θ = sin θ cos θ (∵ y cos θ = x sin θ

   ⇒ x sin θ(sin2 θ + cos2 θ) = sin θ cos θ

   ⇒ x sin θ = sin θ cos θ

   ⇒ x = cos θ ….(1)

   Again x sin θ = y cos θ

   ⇒ cos θ sin θ = y cos θ

   ⇒ y = sin θ ….(2)

   Squaring and Adding equation (1) and (2)

   x^2 + y^2 = cos^2θ + sin^2θ = 1

   x^2 + y^2 = 1

   Reply