已知根号3sinα+cosα=2根号3/3,则cos(2α+π/3)=
问题描述:
已知根号3sinα+cosα=2根号3/3,则cos(2α+π/3)=
答
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/...