sin u =5/13 and pi/2<u<pi
so find cos u = -12/13 as it is in 2nd quadrant.
use cos u= 2 -1 to evaluate cos u/2.
you take only positive value as it is in 1st quadrant.
using that you can find sin u/2 also.
since u/2(pi/4<u/2<pi/2 ) is in 1st quadrant
both cos u/2 and sin u/2 are positive.