三角求值问题sin(π/6 - α)=1/3,则cos(2π/3 + 2α)=? A -7/9 B -1/3 C 1/3 D 7/9 帮讲讲,谢谢.答得好我会加分的.

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三角求值问题sin(π/6 - α)=1/3,则cos(2π/3 + 2α)=?  A -7/9  B -1/3  C  1/3  D 7/9  帮讲讲,谢谢.答得好我会加分的.

三角求值问题sin(π/6 - α)=1/3,则cos(2π/3 + 2α)=? A -7/9 B -1/3 C 1/3 D 7/9 帮讲讲,谢谢.答得好我会加分的.
三角求值问题
sin(π/6 - α)=1/3,则cos(2π/3 + 2α)=? A -7/9 B -1/3 C 1/3 D 7/9 帮讲讲,谢谢.答得好我会加分的.

三角求值问题sin(π/6 - α)=1/3,则cos(2π/3 + 2α)=? A -7/9 B -1/3 C 1/3 D 7/9 帮讲讲,谢谢.答得好我会加分的.
选A.
首先cos(2π/3 + 2α)=cos2(π/3 + α)=2cos(π/3 + α)^2-1
然后sin(π/6 - α)=cos[π/2-(π/6 - α)]=cos(π/3 + α)=1/3
所以cos(2π/3 + 2α)=2cos(π/3 + α)^2-1=2*(1/3)^2-1=-7/9