Prove: Tan^2x - sin^2x = sin^2x tan^2x?

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  • Jasco
    Lv 4
    7 years ago
    Favorite Answer

    LHS=

    tan^2x - sin^2x =(sin^2x / cos^2x) - sin^2x

    = (sin^2x - sin^2x cos^2x) / cos^2x

    = sin^2x (1-cos^2x) / cos^2x since sin^2x = 1 - cos^2x

    = sin^2x (sin^2x) / cos^2x

    = sin^2x tan^2x = RHS

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  • sombra
    Lv 7
    7 years ago

    tan²x-sin²x=sin²x.tan²x

    sin²x/cos²x-sin²x=sin²x.sin²x/cos²x

    (sin²x-sin²x.cos²x):cos²x=sin^4x/cos²x

    sin²x(1-cos²x):cos²x=sin^4x/cos²x

    (sin²x.sin²x);cos²x=sin^4x/cos²x

    sin^4x/cos²x=sin^4x/cos²x

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