Question

If the rate of change of sine and tangent of the same angle are equal, then the angle is

• A. $\frac{(2n\pm 1)\pi }{2},n\in Z$
• B. $n\pi ,$ where $n\in Z$
• C. $2n\pi ,$ where $n\in Z$
• D. $(2n+1)\pi ,$ where $n\in Z$

Answer 1

The correct option is C $2n\pi ,$ where $n\in Z$

$\frac{d}{dt}\left(\sin \theta \right)=\frac{d}{dt}\left(\tan \theta \right)$
$\Rightarrow \cos \theta \frac{d\theta }{dt}={\sec }^2\theta \frac{d\theta }{dt}$
$\Rightarrow {\cos }^3\theta =1$
$\Rightarrow \cos \theta =1$
$\Rightarrow \theta =2n\pi ,$ where $n\in Z$