若sin(π/6-α)=1/3 则cos(2π/3+2α)的值为?

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若sin(π/6-α)=1/3则cos(2π/3+2α)的值为?若sin(π/6-α)=1/3则cos(2π/3+2α)的值为?若sin(π/6-α)=1/3则cos(2π/3+2α)的值为?cos(

若sin(π/6-α)=1/3 则cos(2π/3+2α)的值为?
若sin(π/6-α)=1/3 则cos(2π/3+2α)的值为?

若sin(π/6-α)=1/3 则cos(2π/3+2α)的值为?
cos(2π/3+2α)= - cos(π-(2π/3+2α))
=- cos(π/3-2α)
=- cos(2α-π/3) (公式cos2α=1-2(sinα)^2)
=- (1-2(sin(α-π/6))^2)
因为 sin(π/6-α)=1/3 所以(sin(α-π/6))^2=1/9
故cos(2π/3+2α)= -(1-2*1/9)
=-7/9

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