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

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.