已知函数f(x)已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)求最小正周期
问题描述：
已知函数f(x)已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)求最小正周期
答
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)=√3sin(x+π/2)-sin(x+π)=√3cosx-sinx=2(√3/2cosx-1/2sinx)=2sin(π/3-x)
所以最小正周期为：T=2π
答
原式=√3sin(x+π/2)-sin(x+π)
=√3cosx+sinx
=2sin(x+π/3)
T=2π
答
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
=√3cosx+sinx
=2[sinπ/3*cosx+cosπ/3*sinx]
=2sin(x+π/3)
T=2π/1=2π