If x=cos⁡ θ,y=sin3⁡ θ, then dydx2+yd2ydx2 at ∅=π/2 is

dxdθ=−sin⁡ θ, dydθ=3sin2⁡ θcos⁡ θ→dydx=−3sin⁡ θcos⁡ θ. Differentiating again, we haved2ydx2=−3cos2⁡ θdθdx=3cos⁡ 2θsin⁡ θ.dydx2+yd2ydx2=9sin2⁡ θcos2⁡ θ+sin3⁡ θ3cos⁡ 2θsin⁡ θ =9sin2⁡ θcos2⁡ θ+3sin2⁡ θcos⁡ 2θSo the value of the expression on L.H.S. at θ=π/2 is −3.