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The value of n ∈ I for which the function $f (x) = \frac{\sin nx}{\sin (\frac{x}{n})} has 4 π$ as its period is

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detailed solution

Correct option is A

For n = 2, we havef(x)=sin⁡2xsin⁡x2=2sin⁡xcos⁡xsin⁡x2 =4sin⁡x/2cos⁡x/2cos⁡xsin⁡x2=4cos⁡x2cos⁡xThe period of cos x is 2π and that of cos x2 is 2π1/2=4πHence, the period of f (x) is 4π.

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The value of n ∈ I for which the function f(x)=sin⁡nxsin⁡xn has 4π as its period is

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The value of n ∈ I for which the function $f (x) = \frac{\sin nx}{\sin (\frac{x}{n})} has 4 π$ as its period is