sin2x-12(sinx-cosx)+12=0解方程

sin2x-12(sinx-cosx)+12=0
-(sinx-cosx)^2+1-12(sinx-cosx)+12=o
(sinx-cosx)^2+12(sinx-cosx)+13=0
设sinx-cosx=a
a^2+12a-13=0
a=1
所以sinx-cosx=1
2sin(x-π/4）=1
sin(x-π/4）=1/2
x=kπ+(-1)^k*π/4+π/4,k∈Z