(sin^2(2x/3)+cos^2(2x/3))^2-2sin^2(2x/3)*cos^2(2x/3)=5/8
1-2sin^2(2x/3)*cos^2(2x/3)=5/8
2sin^2(2x/3)*cos^2(2x/3)=3/8
4sin^2(2x/3)*cos^2(2x/3)=3/4
sin^2(4x/3)=3/4
sin(4x/3)=- sqrt(3)/2 или sin(4x/3)=sqrt(3)/2
1)sin(4x/3)=- sqrt(3)/2
(4x/3)=(-1)^(k)*(-Pi/3)+Pik, k ∈ Z
[b]x=(-1)^(k)*(-Pi/4)+(3Pi/4)k, k ∈ Z[/b]
2)sin(4x/3)= sqrt(3)/2
(4x/3)=(-1)^(n)*(Pi/3)+Pik,n ∈ Z
[b]x=(-1)^(n)*(Pi/4)+(3Pi/4)n, n ∈ Z[/b]
О т в е т.
(-1)^(k)*(-Pi/4)+(3Pi/4)k, k ∈ Z
(-1)^(n)*(Pi/4)+(3Pi/4)n, n ∈ Z