已知根号3sinα+cosα=2根号3/3,则cos(2α+π/3)=

已知根号3sinα+cosα=2根号3/3,则cos(2α+π/3)=

已知：√3sinα+cosα=2√3/3,则：√3/2*sinα+1/2*cosα=√3/3＝cos(π/6)*sinα+sin(π/6)*cosα
＝sin(α+π/6)=√3/3；则：[sin(α+π/6)]^2=1/3
因为：cos(2α+π/3)=cos2(α+π/6)＝1-2[(sin(α+π/6)]^2=1-2*1/3=1-2/3=1/3