求证tan^x-sin^2x=tan^2x*sin^2x
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求证tan^x-sin^2x=tan^2x*sin^2x
![求证tan^x-sin^2x=tan^2x*sin^2x](/uploads/image/z/16722599-23-9.jpg?t=%E6%B1%82%E8%AF%81tan%5Ex-sin%5E2x%3Dtan%5E2x%2Asin%5E2x)
tan^x-sin^2x
=sin^2x/cos^2x -sin^2x
=(sin^2x-cos^2x sin^2x)/cos^2x
=sin^2x(1-cos^2x)/cos^2x
=sin^2x sin^2x/cos^2x
=tan^2x sin^2x=右边
=sin^2x/cos^2x -sin^2x
=(sin^2x-cos^2x sin^2x)/cos^2x
=sin^2x(1-cos^2x)/cos^2x
=sin^2x sin^2x/cos^2x
=tan^2x sin^2x=右边
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