17已知函数f(x)=2sinxcos(x+兀/6)-cos2x+m求函数fx最小正周期

问题描述:

17已知函数f(x)=2sinxcos(x+兀/6)-cos2x+m求函数fx最小正周期

f(x)=2sinxcosxcosπ/6-2sinxsinxsinπ/6-cos2x+m
=√3/2*sin2x-1/2+1/2*cos2x-cos2x+m
=√3/2*sin2x-1/2cos2x-1/2+m
=cosπ/6sin2x-sinπ/6cos2x-1/2+m
=sin(2x-π/6)-1/2+m
则最小正周期为2π/2=π