Consider the curve $x=a(\cos \theta+\theta \sin \theta)$ and $y=a(\sin \theta-\theta \cos \theta)$. What is $\frac{d^2 y}{d x^2}$ equal to?

• A

  $\sec ^2 \theta$
• B

  $-\operatorname{cosec}^2 \theta$
• Correct answer
  C

  $\frac{\sec ^3 \theta}{a \theta}$
• D

  None of these

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