Use a sum or difference identity to verify the identity. cos(2pi + theta) = cos theta

Answer 1

cos(2pi+theta)=cos(2pi)cos(theta)+sin(2pi)sin(theta using the sum of two angles identity.

Then, sin(2pi)=0 and the cos(2pi)=1.

Hence the above reduces down to cos(theta), which exactly matches the right side of the starting identity.