Question

If the rate of change of sine of an angle $\theta$ is $K$, then the rate of change of its tangent is

• A. $K^2$
• B. $\frac{1}{K^2}$
• C. $K$
• D. $\frac{1}{K}$

Answer 1

Answer: (B)

$\frac{1}{K^2}$

Given, $\frac{d\left(\sin \theta \right)}{d\theta }=k$
$\Rightarrow \cos \theta =k$
Now, $\frac{d\left(\tan \theta \right)}{d\theta }={\sec }^2\theta$
$=\frac{1}{k^2}$