Verified answer

Not much left to do. Remember that for every integer n, cos(2nπ) = 1 and sin(2nπ) = 0. This follows from the facts that cos(0) = 1, sin(0) = 0, and each of these functions is 2π-periodic. (Note that this is only true if n is an integer.)

So

cos(2π(f + 1)n) = cos(2πfn + 2πn) = cos(2πfn)cos(2πn) - sin(2πfn)sin(2πn)

= cos(2πfn)(1) - sin(2πfn)(0) = cos(2πfn)

as required.

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