= (cos(╥ - a))^2 - (cos(╥/2 - a))^2
= ((-1)^2*cos(a) - sin(a))^2 - (cos(a))^2
= (cos^2(a) - 2cos(a)sin(a) + sin^2(a)) - cos^2(a)
= cos(2a) - 1 - cos^2(a)
= cos(2a) - cos^2(a) - 1.