2cos^22x-2cos2x-sqrt(2)cos2x+sqrt(2)>0
Перегруппируем:
(2cos^22x-2cos2x)-(sqrt(2)cos2x-sqrt(2))>0
2сos2x*(cos2x-1)-sqrt(2)*(cos2x-1) >0
(cos2x-1)*(2cos2x-sqrt(2)) >0
cos2x < 1/2 или cos2x > sqrt(2)/2
(π/3)+2πn < 2x < (5π/3)+2πn, n ∈ Z или (-π/4)+2πk< 2x <(π/4)+2πk, k ∈ Z
(π/6)+πn < x < (5π/6)+πn, n ∈ Z или (-π/8)+πk< x <(π/8)+πk, k ∈ Z
О т в е т. (π/6)+πn < x < (5π/6)+πn, n ∈ Z или (-π/8)+πk< x <(π/8)+πk, k ∈ Z