Question

If $x=\sin t$ and $y=\tan t$, then $\frac{dy}{dx}$ is equal to

• A. ${\cos }^{3}t$
• B. $\frac{1}{{\cos }^{3}t}$
• C. $\frac{1}{{\cos }^{2}t}$
• D. ${\sin }^{2}t$
• E. $\frac{1}{{\sin }^{2}t}$

Answer 1

Answer: (B)

$\frac{1}{{\cos }^{3}t}$

Given, $x=\sin t$ and $y=\tan t$
On differentiating both sides w.r.t. $t$ respectively, we get
$\frac{dx}{dt}=\cos t$ and $\frac{dy}{dt}={\sec }^{2}t$
Therefore, $\frac{dy/dt}{dx/dt}=\frac{{\sec }^{2}t}{\cos t}=\frac{1}{{\cos }^{3}t}$