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

Question

Let $x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}$ and

$y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}\right)$.

Then $\frac{1+\left(\frac{d y}{d x}\right)^{2}}{\frac{d^{2} y}{d x^{2}}}$ at $t=\frac{\pi}{4}$ is equal to :

$\frac{-2 \sqrt{2}}{3}$

$\frac{2}{3}$

$\frac{1}{3}$

$ \frac{-2}{3}$

Solution

Please login to view the detailed solution steps...

Go to DASH