已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为要详细过程
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已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为要详细过程
已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为
要详细过程
已知sin(α+π/4)+sin(α-π/4)=根号2/3 则sin(α-π/4)/1-cos2α-sin2α的值为要详细过程
sin(α+π/4)+sin(α-π/4)
=sinαcosπ/4 + cosαsinπ/4 + sinαcosπ/4 - cosαsinπ/4
=2sinαcosπ/4
=√2 sinα
=√2/3
所以,sinα=1/3
sin(α-π/4)/1-cos2α-sin2α
=[sinαcosπ/4 - cosαsinπ/4]/[2sin²α-2sinαcosα]
=[√2/2sinα - √2/2cosα]/[2sin²α-2sinαcosα]
=[√2/2(sinα -cosα)]/[2sinα(sinα -cosα)]
=(√2/2)/(2sinα)
=3√2/4
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