已知向量a=（2根号3sinx,cosx+sinx),b=(cosx,cosx-sinx）,函数f(x)=a·b,求f(

解
a=(2√3sinx,cosx+sinx),b=(cosx,cosx-sinx）
f(x)=a·b=2√3sinxcosx+cos^2x-sin^2x
=√3sin2x+cos2x
=2sin(2x+π/6)
令2kπ-π/2求f(x)的解析式及周期f(x)=a·b=2√3sinxcosx+cos^2x-sin^2x=√3sin2x+cos2x=2sin(2x+π/6)周期T=2π/2=π