When X belongs to (π/2, π), wx+π/4 belongs to (wπ/2+π/4, wπ+π/4).

The function f(x)=sin(ωx+π/4) monotonically decreases on (π/2, π).

Therefore: 2kπ+π/2 "wπ/2+π/4 "

wπ+π/4《2kπ+3π/2

Get 4k+ 1/2 "w" 2k+5/4.

Therefore, 4k+ 1/2 "2k+5/4 "

k《3/8

k=0

Get 1/2 "w" 5/4.

If you are satisfied, please adopt it! ! thank you