求证(1-2sin2xcos2x)/(cos²2x-sin²2x)=【1-tan(720°+2x)】
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求证(1-2sin2xcos2x)/(cos²2x-sin²2x)=【1-tan(720°+2x)】/【1+(360°=2x)】
左边
=[sin²2x-2sin2xcos2x+cos²2x]/[(cos2x-sin2x)(cos2x+sin2x)]
=[(cos2x-sin2x)²]/[(cos2x-sin2x)(cos2x+sin2x)]
=[cos2x-sin2x)]/[(cos2x+sin2x)] 【分子分母同除以cos2x】
=[1-tan2x]/[1+tan2x]
右边
=[1-tan2x]/[1+tan2x]
左边=右边
证毕.
=[sin²2x-2sin2xcos2x+cos²2x]/[(cos2x-sin2x)(cos2x+sin2x)]
=[(cos2x-sin2x)²]/[(cos2x-sin2x)(cos2x+sin2x)]
=[cos2x-sin2x)]/[(cos2x+sin2x)] 【分子分母同除以cos2x】
=[1-tan2x]/[1+tan2x]
右边
=[1-tan2x]/[1+tan2x]
左边=右边
证毕.
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