y=sin(x-π/6)-cos(x-π/3)
=sinxcosπ/6 -cosxsinπ/6 -cosxcosπ/3 -sinxsinπ/3
=-cosx
所以当x =2kπ时,y有最小值-1；
当x =2kπ+π时,y有最大值1.