已知函数f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3,α为常数求函数f(x)的最小正周期

f(x)=sin(2x+α)+2根3[1+cos(2x+α)]/2-根3
=sin(2x+α)+根3+根3cos（2x+α）-根3
=sin（2x+α）+根3cos（2x+α）
=2sin(2x+α+π/3)
∴T=2π/2=π

原函数=sin(2*(x+a/2))+√3cos(2*(x+a/2))=2*(1/2*sin(2*(x+a/2))+√3/2*cos(2*(x+a/2)))
=2*(cos(pi/3)*sin(2*(x+a/2))+sin(pi/3)*cos(2*(x+a/2)))
=2*sin(2*(x+a/2)+pi/3);
pi就是圆周率

f(x)=2sin(x+α/2)cos(x+α/2)+2√3cos^2(x+α/2)-√3
f(x)=sin(2x+α)+2√3[cos(2x+α)+1]/2-√3
f(x)=sin(2x+α)+√3[cos(2x+α)+1]-√3
=sin(2x+α)+√3cos(2x+α)
=2×[1/2sin(2x+α)+√3/2cos(2x+α)]
=2[sin(2x+α)·cosπ/3+cos(2x+α)·sinπ/3]
=2sin(2x+α+π/3) ∴ ω = 2
T=2π/|ω|=π