已知函数f(x)=2sinxsin(x+π/3) 求函数f(x)的最大值

f(x)=2sinxsin(x+π/3) =2sinx(sinxcosπ/3+cosxsinπ/3) =2sinx(1/2*sinx+√3/2*cosx) =sin²x+√3sinxcosx =(1-cos2x)/2 + √3*sin2x/2 =1/2-cos2x / 2 + √3*sin2x/2 =1/2-cosπ/3cos2x+sinπ/3sin2x =1/