根号2倍(sin(2x-π/4)+1)/1+tan(x)
=(sin(2x)-cos(2x)+1)/(1+tan(x))
=(2sin(x)*cos(x)+2sin(x)^2)/(1+tan(x))
=2sin(x)*cos(x)
又∵sin(x)+cos(x)=2/3
∴2sin(x)*cos(x)=(2/3)^2-1=-5/9
∴根号2倍(sin(2x-π/4)+1)/1+tan(x)=-5/9