化简 cos2a/(1-2tana*cos^2a)

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化简 cos2a/(1-2tana*cos^2a)
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化简 cos2a/(1-2tana*cos^2a)
化简 cos2a/(1-2tana*cos^2a)

化简 cos2a/(1-2tana*cos^2a)
cos2a/(1-2tana*cos^2a)
=cos2a/(1-2sinacosa)
=(cos²a-sin²a)/(cos²a-2sinacosa+sin²a)
=(cosa-sina)(cosa+sina)/(cosa-sina)²
=(cosa+sina)/(cosa-sina)
=√2(sinacosπ/4+cosasinπ/4)/[√2(cosacosπ/4-sinasinπ/4)]
=sin(a+π/4)/cos(a+π/4)
=tan(a+π/4)

=cos2a/1-2sinacosa
=cos2a/sin^2a+cos^2a-2sinacosa
=(cos^2a-sin^2a)/sin^2a+cos^2a-2sinacosa
分子分母都除以cos^2a
=(1-tan^2a)/tan^2a+1-2tana
=(1-tana)(1-tana)/(tana-1)^2
=1