F(X)=2√3sinx/2*cosx/2-(cos²x/2-sin²x/2) =√3sinx-cosx=2(√3/2sinx-1/2cosx)=2(sinxcosπ/6-sinπ/6cosx)=2sin(x-π/6)当 x-π/6=2kπ+π/2,即 x=2kπ+2π/3 (k∈Z) 时F(X) 最大 = 2