已知函数fx=cosx·sin(x+π/3)-√3cos^2x+√3/4x∈r求fx的最小正周期

Question

已知函数fx=cosx·sin(x+π/3)-√3cos^2x+√3/4x∈r求fx的最小正周期

Answer 1

f(x)=cosx·sin(x+π/3)-√3cos²x+√3/4
=sinxcosxcosπ/3+cos²xsinπ/3-√3cos²x+√3/4
=1/4sin2x+√3/4cos2x
=1/2[sin2xcosπ/3+sinπ/3cos2x)]
=1/2sin(2x+π/3)
f(x)的最小正周期：T=2π/2=π