cos(2pi - a) = cos(-a) = cos(a)

cos(a) + sin(a) = √2 (cos(a) * √2/2 + sin(a) * √2/2) = √2 (cos(a) * sin(pi/4) + sin(a) * cos(pi/4)) = √2 sin (a + pi/4)

√2 sin(a + pi/4) + 1 = √2 sin(a + pi/4) + √2 sin(pi/4) = 2√2 sin(a/2 + pi/4) * cos(a/2)