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
聯(lián)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
答題不易,且回且珍惜
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