Use the angle-sum identity for cosine:
You may also think of the unit circle. Pick an arbitrary point on the circle. The counter-clockwise angle to the radius at this point as measured from the positive x-axis is the angle . The x-coordinate of this point is . To add radians to this angle, go to the point on the opposite side of the circle, on the other end of the diameter. Can you see what relation the new x-coordinate will always have with the original?