For example: y=sin^2(t)(2cos(2t)+2cos(4t)+2cos(6t)+2cos(8t)+1)

The period of a sin/cos function is 2Pi/B, where B is the coefficient of the argument inside the sin/cos function. However in this case, there are multiple periodic functions. Do I have to reduce them to a single periodic function using identities and then apply the 2Pi/B expression?