Question 431469
{{{cos(2x) = cos^2(x) - sin^2(x) = cos^2(x) + sin^2(x) - 2sin^2(x) = 1 - 2sin^2(x)}}}


{{{cos(2x) - 1 = -2sin^2(x)}}}


{{{sin^2(x) = (1 - cos(2x))/2}}}


{{{sin(x) = sqrt((1 - cos(2x))/2)}}}


Replacing x with u/2,


{{{sin(u/2) = sqrt((1 - cos(u))/2)}}} (however you must be careful what quadrant u and u/2 are in, because it could be positive or negative).