Cos(2x-π/2)=√3sinx
sin2x-√3sinx=0
2sinxcosx-√3sinx=0
sinx(2cosx-√3)=0
sinx=0⇒x=πn,n∈z
π≤πn≤5π/2
1≤n≤5/2
n=1⇒x=π
n=2⇒x=2π
cosx=√3/2⇒x=-π/6+2πk,k∈z U x=π/6+2πm,m∈z
π≤-π/6+2πk≤5π/2
6≤-1+12k≤15
7≤12k≤16
7/12≤k≤4/3
k=1⇒x=-π/6+2π=11π/6
π≤π/6+2πm≤5π/2
6≤1+12m≤15
5≤12m≤14
5/12≤m≤7/6
m=1⇒x=π/6+2π=13π/6