(cos^2 2x－sin^2 2x)/(1－tan2x)=(1+2sin2xcos2x)/(1+tan2x)

来源：学生作业帮助网 编辑：作业帮 时间：2024/11/17 02:39:54

(cos^2 2x－sin^2 2x)/(1－tan2x)=(1+2sin2xcos2x)/(1+tan2x)
(cos^2 2x－sin^2 2x)/(1－tan2x)=(1+2sin2xcos2x)/(1+tan2x)

(cos^2 2x－sin^2 2x)/(1－tan2x)=(1+2sin2xcos2x)/(1+tan2x)
(1+2sin2xcos2x)/(cos²2x-sin²2x)
= (sin²2x+cos²2x+2sin2xcos2x)/(cos²2x-sin²2x)
= (sin2x+cos2x)²/[(cos2x+sin2x)(cos2x-sin2x)]
= (sin2x+cos2x)/(cos2x-sin2x)
= (1+tan2x)/(1-tan2x)【分子分母同除cos2x】
移项得:(cos^2 2x－sin^2 2x)/(1－tan2x)=(1+2sin2xcos2x)/(1+tan2x)

前面分子用平方差公式打开，分母化成用正余弦表示。后面的1用sin^22x+cos^22x表示，平方和，分母用正余弦表示 约分就出来了。

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