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已知sin(π/4 +α)*sin(π/4 -α)=1/6,α∈(π/2,π),求sin4α
人气:120 ℃ 时间:2020-06-13 01:32:15
解答
sin(π/4 -α)=cos[π/2-(π/4 -α)]=cos(π/4 +α)
sin2(π/4 +α)=2sin(π/4 +α)*sin(π/4 -α)=1/3=cos2α
α∈(π/2,π),2α∈(π,2π)所以sin2α<0
sin2α=-(2根号2)/3
sin4α=-(4根号2)/9
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