Question

If $tan\left(k+1\right)\theta =tan\theta$ , then the set of all the values of $\theta$ is

• A. $\left\{n\pi :n\in I\right\}$
• B. $\left\{\frac{n\pi }{2}:n\in I\right\}$
• C. $\left\{\frac{n\pi }{k}:n\in I\right\}$
• D. $\left\{\frac{n\pi }{4}:n\in I\right\}$

Answer 1

Answer: (C)

As we know the general solution of the equation
$tanx=tan\alpha$ is given by $x=n\pi +\alpha ,n\in I$
Hence, the solution of the equation, $tan\left(k+1\right)\theta =tan\theta$
is given by $\left(k+1\right)\theta =n\pi +\theta ,n\in I.$
$\Rightarrow k\theta =n\pi ,n\in I$ .
$\therefore \theta \in \frac{n\pi }{k},n\in I$