1 - cos(α) = 2·sin^2(α/2)
Subst. x = α/2
1 - cos(2·x) = 2·sin^2(x)
1 - cos(x + x) = 2·sin^2(x)
1 - (cos(x)·cos(x) - sin(x)·sin(x)) = 2·sin^2(x)
1 - cos^2(x) + sin^2(x) = 2·sin^2(x)
sin^2(x) + cos^2(x) = 1 --> sin^2(x) = 1 - cos^2(x)
sin^2(x) + sin^2(x) = 2·sin^2(x)