I came across the following question: Let $f(x)=\cos(nx) \sin(\frac{5x}{n})$ have a period of $3\pi$. Find the integral value of $n$
The traditional way of solving this is to equate $f(x) with f(x+3π)$ and then proceed.
However I find this way to be cumbersome and not so fun to do.
We are aware of the facts like $f(p)+f(q)$ will have a period which will be the L.C.M. of the individual periods,
$af(x)$ will have it's period unaffected by the constant a,
And so on
Is there any way I can find the period of two functions multiplied with each other in these forms?