已知向量a=(sin(x+π/6),cosx),b=(cosx,cos(x-π/3)),函数f(x)=向量a...
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f(x)=sin(x+π/6)cosx+cosxcos(x-π/3)-1/2
cos(x-π/3)=cos(π/3-x)
=cos[π/2-(x+π/6)]
=sin(x+π/6)
所以，f(x)=sin(x+π/6)cosx+cosxsin(x+π/6)-1/2
=sin(x+π/6+x)-1/2
=sin(2x+π/6)-1/2
所以，最小正周期T=2π/2=π
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