I need to find the period of the function $$\large{\frac{\sin (\sin {nx})}{\tan{\frac{x}{n}}}}$$.
According to me, the period of $\sin (\sin (nx))$ should be $\large{\frac{2\pi}{n}}$ and the period of $\large{\tan{\frac{x}{n}}}$ should be $\large{\frac{\pi}{\frac{1}{n}}=\pi n}$.
So the period should be the LCM, that is $\color{red}{\large{2\pi n}}$, right?
But Wolfram Alpha says the function is not periodic. What is the mistake I'm making here?