Q203 / 270 · NDA 2010 (Phase 2) · Mathematics

If $x=\cos (2 t)$ and $y=\sin ^2 t$, then what is $\frac{d^2 y}{d x^2}$ equal to?

  • Correct answer
    A
    0
  • B
    $\sin (2 t)$
  • C
    $-\cos (2 t)$
  • D
    $-1 / 2$

Solution

$\begin{aligned} & x=\cos ^{(2 t)} \text { and } y=\sin ^2 t \\ & \therefore \frac{d x}{d t}=-2 \sin 2 t \text { and } \frac{d y}{d t}=2 \sin t \cdot \cos t \\ & \therefore \frac{d y}{d x}=\frac{2 \sin t \cdot \cos t}{-4 \sin t \cdot \cos t}=-\frac{1}{2} \\ & \therefore \frac{d^2 y}{d x^2}=0\end{aligned}$

Hence, the correct answer is option: 'A'.

Relevant Questions