令sinx-cosx=a,则a^2=sin^2x+cos^2x-2sinxcosx=1-2sinxcosx,所以sinxcosx=(1-a^2)/2,故原式可变形为：a^2-2a+1=0,解得a=sinx-cosx=根号2倍的sin(x-45度)=1,解得x∈360k+135度,k∈Z,有些符号不会打,请谅解...