由倍角公式：sin2x=2sinxcosx,cos2x=2cos²x-1得：sinxcosx=(1/2)sin2x,cos²x=(1+cos2x)/2所以,y=(1/2)sin2x-(1/2)cos2x-1/2=(√2/2)sin(2x-π/4)-1/2当sin(2x-π/4)=1时,y有最大值,y(max)=(√2-1)/2...