Determine whether or not each of the following signals is periodic if signal is periodic determine the fundamental period (note that these are discrete not continuous signals)

1. $\displaystyle x(n) = \cos^3(\frac{\pi(n)}{8})$

2. $\displaystyle x(n) = \cos(\frac{n}{2})\cos(\frac{\pi(n)}{4})$

do i need to do trigonometric identities ? I read in the book that the sum of two periodic signals is "periodic" and it does not mention "product" where the given equation above is the case

An easy example to guide the helpers is this

x(n) = cos(2n)

f = w/(2pi) = 2/(2pi) = 1/pi ----> this is an irrational number hence it is not periodic