Let x(t)=2 √ 2 cos t √(sin 2 t) and y(t)=2 √ 2 sin t √(sin 2 t), t ∈(0, (π)/2). Then (1+((d y)/(d x))^2)/((d^2 y)/(d x^2)) at t=(π)/4 is equal to:

Let $\displaystyle x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}$ and $\displaystyle y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}\right)$. Then $\displaystyle \frac{1+\left(\dfrac{d y}{d x}\right)^2}{\dfrac{d^2 y}{d x^2}}$ at $\displaystyle t=\frac{\pi}{4}$ is equal to :