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](/uploads/image/z/7106823-63-3.jpg?t=%E5%B7%B2%E7%9F%A5sin%28%CE%B1%2B%CF%80%2F4%29%2Bsin%28%CE%B1-%CF%80%2F4%29%3D%E6%A0%B9%E5%8F%B72%2F3+%E5%88%99sin%28%CE%B1-%CF%80%2F4%29%2F1-cos2%CE%B1-sin2%CE%B1%E7%9A%84%E5%80%BC%E4%B8%BA%E8%A6%81%E8%AF%A6%E7%BB%86%E8%BF%87%E7%A8%8B)
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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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