Evaluate ∑k=0n(nk)cos(kx)\sum_{k=0}^{n} \binom{n}{k} \cos(kx)∑k=0n(kn)cos(kx) using the property of complex exponentials.
2ncosn(x/2)cos(nx/2)2^n \cos^n(x/2) \cos(nx/2)2ncosn(x/2)cos(nx/2)
2nsinn(x/2)cos(nx/2)2^n \sin^n(x/2) \cos(nx/2)2nsinn(x/2)cos(nx/2)
cosn(x)\cos^n(x)cosn(x)
ncos(nx)n \cos(nx)ncos(nx)