若sin((π/6)-α)=1/3,则cos((2π/3)+2α)等于多少?
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若sin((π/6)-α)=1/3,则cos((2π/3)+2α)等于多少?
若sin((π/6)-α)=1/3,则cos((2π/3)+2α)等于多少?
若sin((π/6)-α)=1/3,则cos((2π/3)+2α)等于多少?
sin((π/6)-α)=1/3,
而sin((π/6)-α)=cos[π/2-((π/6)-α))]
= cos((π/3)+α),
∴cos((π/3)+α)=1/3.
所以cos((2π/3)+2α)= cos[2((π/3)+α)]
= 2cos²((π/3)+α)-1
=-7/9.
由题知,
sin((π/6)-α)=1/3
所以,
cos((π/6)-α)=±2√2/3
所以,
cos((2π/3)+2α)
=cos[π/2-((π/3)-2α)]
=sin((π/3)-2α)
=2sin((π/6)-α)cos((π/6)-α)
=±4√2/9
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