已知向量a=(sinx,-1),向量b=(√3cosx ,-½),函数f(x)=(a+b)a-2 (1)求函数的最小正周期9

a+b＝sinx+√3cosx -3/2
(a+b)a=(sinx+√3cosx )sinx+0
f(x)=(a+b)a-2 =(sinx+√3cosx )sinx-2
=sin^2x+√3cosx sinx-2
=1/2(1-cos2x )+√3/2 sin2x-2
=√3/2 sin2x-1/2cos2x -3/2
=sin(2x-π/6)-3/2
T=2π/2=π