已知cos(α-π/6)+sinα=(4倍根号3)/5,则sin(α+7π/6)=

cos(α-π/6)+sinα=4√3/5cos(α-π/6)+cos(π/2-α)=4√3/52cos{[(α-π/6)+(π/2-α)]/2}*cos{[(α-π/6)-(π/2-α)]/2}=4√3/52cosπ/6*cos(α-π/3)=4√3/52√3/2*sin(α+π/6)=4√3/5sin(α+π/6)=4/5sin(α+7π/6)=-sin(α+π/6)=-4/5