Consider if is periodic then where is a period.

Now we have as is a function with periodicity we must have and are both of the form where is an integer not necessarily same in both the cases. In first case its enough if ,and in the second case if where where is the set of integers. Therefore if to be the fundamental period then we are fine with it.

Multiplication of functions can be handled on the same lines.

Now try solving the following problem instead

Kalyan.