2sin²x+2cos²2x-1=0
2(1-cos2x)/2+2cos²2x-1=0
2cos²2x-cos2x=0
cos2x(2cos2x-1)=0
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
5π/2≤π/4+πn/2≤3π
10≤1+2n≤12
9≤2n≤11
4,5≤n≤5,5
n=5 x=π/4+5π/2=11π/4
cos2x=1/2⇒2x=+-π/3+2πn⇒x=+-π/6+πn
5π/2≤-π/6+πn≤3π
15≤-1+6n≤18
16≤6n≤19
2 2/3≤n≤3 1/6
n=3 x=-π/6+3π=17π/6
5π/2≤π/6+πn≤3π
15≤-1+6n≤18
14≤6n≤17
2 1/3≤n≤2 5/6
нет решения
Ответ x=11π/4 U x=17π/6