已知α为锐角,且tanα=1/2,求(sin2αcosα-sinα)/(sin2αcos2α) 的值每一步都要详细
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![已知α为锐角,且tanα=1/2,求(sin2αcosα-sinα)/(sin2αcos2α) 的值每一步都要详细](/uploads/image/z/2533962-66-2.jpg?t=%E5%B7%B2%E7%9F%A5%CE%B1%E4%B8%BA%E9%94%90%E8%A7%92%2C%E4%B8%94tan%CE%B1%EF%BC%9D1%2F2%2C%E6%B1%82%28sin2%CE%B1cos%CE%B1-sin%CE%B1%29%2F%28sin2%CE%B1cos2%CE%B1%29+%E7%9A%84%E5%80%BC%E6%AF%8F%E4%B8%80%E6%AD%A5%E9%83%BD%E8%A6%81%E8%AF%A6%E7%BB%86)
已知α为锐角,且tanα=1/2,求(sin2αcosα-sinα)/(sin2αcos2α) 的值每一步都要详细
已知α为锐角,且tanα=1/2,求(sin2αcosα-sinα)/(sin2αcos2α) 的值
每一步都要详细
已知α为锐角,且tanα=1/2,求(sin2αcosα-sinα)/(sin2αcos2α) 的值每一步都要详细
tanα=1/2===>sinα=1/√5,cosα=2/√5
∴原式=1-sinα/[2sinαcosα(1-2sin²α)]
=1-(1/√5)/[2(1/√5)(2/√5)(1-2/5)]
=1-(1/√5)/[(4/5)*(3/5)]
=1-(1/√5)(25/12)
=1-5√5/12
原式=1-sinα/[2sinαcosα(1-2sin²α)]
=1-(1/√5)/[(4/5)*(3/5)]
=1-5√5/12