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1-tan^2/1-cot^2 = 1-sec^2...pls prove?

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1-tan^2/1-cot^2 = 1-sec^2...pls prove?

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  1. (1-tan^2 ) / (1-cot^2)

    =  (1-tan^2 ) / {1- 1/ tan^2}

    = ( 1 - tan^2 )/ { ( tan^2 - 1)/ tan^2 }

    = -tan^2

    = - ( sec^2 - 1)

    =  1 - sec ^2


  2. (1-tan^2)/(1-cot^2)

    change it into sin and cos

    1-sin^2/cos^2

    -------------------

    1-cos^2/sin^2

    =cos^2-sin^2

    ------------------

        cos^2

    --------------------------

    sin^2-cos^2

    ----------------

    sin^2

    =cos^2-sin^2               sin^2

    --------------------   x        -----------------

    cos^2                         sin^2-cos^2

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

    --------------------   x        -----------------

    cos^2                        -( sin^2-cos^2)

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

    --------------------   x        -----------------

    cos^2                        ( cos^2-sin^2)

    = -(  sin^2)

    ----------------

    cos^2        

    =-tan^2

    =-(sec^2-1)

    =1-sec^2

    Please rate me if u find my answer helpful.:))))

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