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

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