Representing cos(npi/2) in general form

[nutcase21]

hi i am currently trying to solve a Fourier series question and i realize for example cos(npi) can be represented as (-1)ⁿ.

So i was wandering is there anyway to represent cos(npi/2) to a general form too?

 

[Office_Shredder]

i suppose something like
(1+(-1)ⁿ)/2*(-1)^n/2

 

[nutcase21]

OIC thnks.

is there any tricks to getting the general form?