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Math Help - Trig. Eqautions

  1. #1
    Junior Member CONFUSED_ONE's Avatar
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    Trig. Eqautions

    how would you simplify this trig. equation.

    (1+sec2x)(cot2x)

    *note: the blue 2's are squared.

    i did it and the final answer i got is 2cot2x
    Last edited by CONFUSED_ONE; May 5th 2006 at 05:22 AM. Reason: Change solve into Simplify
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  2. #2
    TD!
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    There is nothing to solve. You either forgot something, or perhaps meant 'simplify'?
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  3. #3
    Junior Member CONFUSED_ONE's Avatar
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    lol. Yes, I meant simplify.
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  4. #4
    TD!
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    Then your answer is wrong. I don't think there's a lot to simplify though, depends on where you want to go with it. You can simplify it to cot²x+csc²x for example.
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  5. #5
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    Quote Originally Posted by CONFUSED_ONE
    how would you simplify this trig. equation.

    (1+sec2x)(cot2x)

    *note: the blue 2's are squared.

    i did it and the final answer i got is 2cot2x
    Here is one way.

    Let U = (1 +sec^2(x))*cot^2(x)
    So,
    U = cot^2(x) +[sec^2(x) *cot^2(x)]
    U = cot^2(x) + [1/cos^2(x) *cos^2(x)/sin^2(x)]
    U= cot^2(x) +1/sin^2(x)
    U = cot^2(x) +csc^2(x) --------(i)

    The trig identity,
    sin^2(x) +cos^2(x) = 1
    Divide both sides by sin^2(x),
    1 +cot^2(x) = csc^2(x)
    Rearrange,
    1 = -cot^2(x) +csc^2(x) ---------(ii)

    Add (i) and (ii),
    U +1 = 2csc^2(x)
    Hence,
    U = 2csc^2(x) -1
    Therefore,
    (1 +sec^2(x))*cot^2(x) = 2csc^2(x) -1 -----------answer.

    Or,
    Subtract (ii) from (i),
    U -1 = 2cot^2(x)
    Hence,
    U = 2cot^2(x) +1
    Therefore,
    (1 +sec^2(x))*cot^2(x) = 2cot^2(x) +1 -----------answer.
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