If $n \in N$ and the period of $\frac{\cos n x}{\sin \left(\frac{x}{n}\right)}$ is $4 \pi$, then $n$ is…
If $n \in N$ and the period of $\frac{\cos n x}{\sin \left(\frac{x}{n}\right)}$ is $4 \pi$, then $n$ is equal to
$4$
$3$
$2$
$1$
Solution
Given that period of $\frac{\cos n x}{\sin \left(\frac{x}{n}\right)}$ is $4 \pi$.
We know
Period of $\quad \cos n x=\frac{2 \pi}{n}$
and period of $\sin \left(\frac{x}{n}\right)=2 n \pi$
$\begin{array}{ll}\therefore \text { Period of } & \frac{\cos n x}{\sin \left(\frac{x}{n}\right)} \text { is } 2 n \pi . \\ \Rightarrow & 2 n \pi=4 \pi \Rightarrow n=2\end{array}$