f(x)=2sinxcosx-2sin^2x=sin2x+cos2x-1=√2sin(2x+π/4)-1
∴当sin(2x+π/4)=1时,f(x)取得最大值=√2-1
sin(2x+π/4)=1 2x+π/4=2kπ+π/2 x=kπ+π/8 {x I x=kπ+π/8}