解: a.b=2√3sinx*cosx+(cos+sinx)(cosx-sinx)=√3sin2x+cos²x-sin²x
a.b=√3sin2x+cos2x=2sin(2x+π/6)=1
sin(2x+π/6)=1/2
2x+π/6=2kπ+π/6或2x+π/6=2kπ+5π/6
x=kπ或x=kπ+π/3,k∈Z
解: a.b=2√3sinx*cosx+(cos+sinx)(cosx-sinx)=√3sin2x+cos²x-sin²x
a.b=√3sin2x+cos2x=2sin(2x+π/6)=1
sin(2x+π/6)=1/2
2x+π/6=2kπ+π/6或2x+π/6=2kπ+5π/6
x=kπ或x=kπ+π/3,k∈Z