Q65 / 160 · AP EAMCET 2004 · Mathematics

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

  • A
    $4$
  • B
    $3$
  • Correct answer
    C
    $2$
  • D
    $1$

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 $\sin \left(\frac{x}{n}\right)=2 n \pi$ $\begin{array}{ll}\therefore \text { Period of } & \frac{\cos n x}{\sin \left(\frac{x}{n}\right)} \text { is } 2 n \pi . \\ \Rightarrow & 2 n \pi=4 \pi \Rightarrow n=2\end{array}$

Hence, the correct answer is option: 'C'.

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