tan(π/6-α)=sin(π/6-α)/cos(π/6-α)=1/3
cos(π/6-α)=sin(α+π/3)=3cos(π/6-α)=3cos(α+π/3)
即sin(α+π/3)=3cos(α+π/3)①
cos^2(α+π/3)+sin^2(α+π/3)=1②
联立一②得
cos^2(α+π/3)=1/10
cos(2α+2π/3)=2cos^2(α+π/3)-1
=1/5-1=-4/5
答题不易,且回且珍惜
如有不懂请追问,若明白请及时采纳,祝愉快O(∩_∩)O~~~会了