cosx- sin x= -1/2,

cosx- sin x= -1/2,
cosx- sin x= -1/2,

cosx- sin x= -1/2,
cosx- sin x= -1/2
√2(√2/2*cosx-√2/2* sin x)= -1/2
√2(cosπ/4cosx-sinπ/4sin x)= -1/2
√2cos(x+π/4)= -1/2
cos(x+π/4)= -1/(2√2)
cos(x+π/4)= -√2/4

即sinx-cosx=1/2
√2sin(x-π/4)=1/2
sin(x-π/4)=√2/4
x-π/4=2kπ+arcsin(√2/4)，x-π/4=2kπ+π-arcsin(√2/4)
所以x=2kπ+π/4+arcsin(√2/4)，x=2kπ+5π/4-arcsin(√2/4)