重生商业小说排行榜:已知(4sin^2) x-(cos^2)x-6sinx+3cosx=0,求(cos2x-cos^2 x)/(1-cot^2 x)的值。

来源：百度文库编辑：高校问答时间：2024/05/03 05:15:43

两头一起走：
(cos2x-cos^2 x)/(1-cot^2 x)=(cos^2 x-1)/(1-cot^2 x)（倍角）=sin^2 x(cos^2 x-1)/(sin^2 x-cos^2 x)=sin^4 x/cos(2x)=(1-cos2x)^2/(4*cos2x)
再由已知的(4sin^2) x-(cos^2)x-6sinx+3cosx=0 推出
(2sinx+cosx)(2sinx-cosx)=3*(2sinx-cosx) =>(1)2sinx-cosx=0 (2)2sinx+cosx=3(显然不成立，舍去)。所以tanx=1/2 =>cos2x=3/5 => (cos2x-cos^2 x)/(1-cot^2 x)=(1-cos2x)^2/(4*cos2x)=1/15

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