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
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