starting to learn trig and I keep running into problems. Could I please get some help solving this.

Question

sin(2pi + theta)= sin theta

Answer 1

sin(2*pi) * cos(theta) + cos(2*pi)*sin(theta) = sin(theta)

sin(2*pi) = 0, so the first term vanishes

cos(2*pi) = 1 so the second term is just sin(theta)

So the equation becomes the identity sin(theta) = sin(theta)

So all reals