f(x)=2sinx(cosx-sinx)=2sinxcosx-2(sinx)²+1-1=sin2x+cos2x-1=√2sin2xcosπ/4+cos2xsinπ/4-1=√2sin（2x+π/4）-1T=2π/2=π对称轴：2x+π/4=π/2+kπ,k∈Z,整理得：x=π/8+kπ/2,k∈Z对称中心：2x+π/4=kπ...