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    ellenegaudet's Avatar
    ellenegaudet Posts: 1, Reputation: 1
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    #1

    Jan 11, 2011, 06:00 PM
    How do you prove this identity?
    (tan^4x)-(tan^2x)(sec^2x) = -tan^2x
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    Unknown008 Posts: 8,076, Reputation: 723
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    #2

    Jan 11, 2011, 10:07 PM

    You can do it in a very simple way starting by factoring tan^2x.





    Then, recall the pythagoras' identify:



    Divide this by cos^2x to give:



    This means that

    Substitute that in



    What do you get? :)
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