y=sinxcosπ/6+cosxsinπ/6-cosxcosπ/6-sinxsinπ/6
=(√3-1)/2*(sinx-cosx)
=(√3-1)/2*√2sin(x-π/4)
所以sin=1
即x-π/4=2kπ+π/2
x=2kπ+3π/4时
最大值=(√3-1)/2*√2=(√6-√2)/2
y=sinxcosπ/6+cosxsinπ/6-cosxcosπ/6-sinxsinπ/6
=(√3-1)/2*(sinx-cosx)
=(√3-1)/2*√2sin(x-π/4)
所以sin=1
即x-π/4=2kπ+π/2
x=2kπ+3π/4时
最大值=(√3-1)/2*√2=(√6-√2)/2