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    Kpocky's Avatar
    Kpocky Posts: 2, Reputation: 1
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    #1

    Feb 14, 2013, 08:44 PM
    Verifying identities trig
    csc^2 x-1/csc^2x=cos^2x

    Please explain step by step
    ebaines's Avatar
    ebaines Posts: 12,131, Reputation: 1307
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    #2

    Feb 15, 2013, 07:38 AM
    First of all the identity you wrote is incorrect, because:


    and this does not equal

    However, I suspect what you meant is this:

    (csc^2(x) - 1)/csc^2x =cos^2x

    It is imperative that you use parentheses properly!

    As usual with these types of problems, start by replacing any functions of tan, cot, sec, and csc with their sin and cos equivalents. In this case you replace csc(x) with 1/sin(x) and the left hand side becomes



    Then simply - multiply through by and apply the identity .

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