(sin(2x)+cos(2x))^2=1
(sin(2x)+cos(2x))^2-1=0
(sin(2x)+cos(2x)+1)(sin(2x)+cos(2x)-1)=0
(2sqrt(2) sin(x + π/4) cos(x))(2 sqrt(2) sin(π/4 - x) sin(x))=0
make each factor =0
2sqrt(2) sin(x + π/4) cos(x)=0 if sin(x + π/4) =0 or cos(x)=0
and
2 sqrt(2) sin(π/4 - x) sin(x))=0 if sin(π/4 - x)=0 or sin(x)=0
sin(x + π/4) =0 for x = π n +π/4, n element Z
cos(x)=0 for x = π n - π/2, n element Z
sin(π/4 - x)=0 for x = π n + (3π)/4, n element Z
sin(x)=0 for x = π n, n element Z -> Integer solution is x=0
general solutions are:
x= π*n
x=π*n+π/4
x=π/2+2π*n
x=3π/4+π*n
