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.
@saravananbs
Why not learn to post in symbols? You can use LaTeX tags
You do understand that this is not a homework service?
[tex] \sin\left(\frac{u}{2}\right)=\sqrt{\dfrac{1-\cos(u)}{2}} [/tex]
gives