sin2x-12(sinx-cosx)+12=0
1-（sinx-cosx)^2-12(sinx-cosx)+12=0
sinx-cosx=t=√2sin(x-45),属于0到π闭
-√2/2<=t<=√2
t^2+12t-13=0
(t-1)(t+13)=0
t=1或t=-13舍
t=√2sin(x-∏/4)=1
x=∏/2或x=∏