Question

If x = 1 ${\sec }^2\theta ,$ y = a ${\tan }^2\theta$ then $\frac{d^{2}y}{d{x}^2}$ =

• A. 0
• B. 2a
• C. 4
• D. 1

Answer 1

Answer: (A)

$\frac{dx}{d\theta }=2ase{c}^2\theta tan\theta$
$\frac{dy}{d\theta }=2atan\theta se{c}^2\theta$
$\therefore \frac{dy}{dx}=\frac{dy}{\frac{d\theta }{\frac{dx}{d\theta }}}=\frac{2atan\theta .se{c}^2\theta }{2atan\theta se{c}^2\theta }=1\therefore \frac{d^{2}y}{d{x}^2}=0$