Question

If x = cos θ and y = sin³ θ, then prove that: yd²y/dx² + (dy/dx)² = 3sin² θ(5cos² θ - 1), 

Answer 1

Here,

x = cosθ and y = sin³θ

Differentiating w.r.t .θ, we get

Differentiating w.r.t . x, we get 

= RHS

Answer 2

x = cos θ and y = sin³ θ