Find sinθ/2 and sin2θ if cosθ=8/17 and 0≤θ≤π/2

Try this option (replace, pls, a↔θ):
rule: if a∈[0;90°], then cos(a)>0, sin(a)>0, sin(a/2)>0, cos(a/2)>0 and tg(a)>0.
1. for sin(a/2):
using 'cos(a)=1-2sin²(a/2)', ⇒ 

2. for sin(2a):
sin(2a)=2*sin(a)cos(a), where sin(a)=√(1-cos²(a))=15/17.