Question

is cos(2*pi*n) = 1?

Answer 1

period of \(\cos(x)\) is \(2\pi\), therefore adding/subtracting an integer multiple of \(2\pi\) wont change the function's value :
\[\cos(x) = \cos(x\pm2n\pi)\]

Answer 2

\[\cos(2n\pi) = \cos(0+2n\pi) = \cos(0) = 1\]