let the period of f(x) be T and period of g(x) be T1

now period of f(x) +g(x)   will be equal to lcm of T and T1

but what is the period of f(x)/g(x)

how to find it??????????????????

Q. If the period of sin(nx) / tan(x/n) nbelongs to I

is 6pie

then

find n???????

well sin(nx) period is 2pie/n

tan(x/n) period is pie n

how to proceed from here

But he has already given the period. Why dont you just substitute it to find n?

I'm not too sure but I think the period of f(x)/g(x) is once again lcm of periods of f(x),g(x).For example,Let us take the problem that you have given,

The period of sin(nx) is 2pi/n and that of tan(x/n) is npi.Now,the lcm of 2pi/n and npi is 2npi which is given to be 6pi.Hence,the value of n is 3.

Is the answer correct?