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Math Help - Establishing Trig Identities

  1. #1
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    Establishing Trig Identities

    Ive been working on this problem for quite some time now and i haven't been able to figure it out.

    tanU(cscU-sinU)=cosU

    this is what ive done so far

    tanU*cscU - tanU*sinU

    (sinU/cosU)*(1/sinU) - (sinU/cosU)*sinU

    (1/cosU) - (sin^2U/cosU)

    (1-sin^2(U)/cosU)

    Half Angles Formula
    (1-1+cos(2U))/2cosU

    cos(2U)/2cosU

    Double angles Formula
    (2cos^2(U)-1)/2cosU

    cosU-1

    cosU-1 =/= cosU


    ands so i end up with that pesky -1 out there.

    so what am i doing wrong?
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  2. #2
    Member mathemagister's Avatar
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    Quote Originally Posted by skipmonkey View Post
    Ive been working on this problem for quite some time now and i haven't been able to figure it out.

    tanU(cscU-sinU)=cosU

    this is what ive done so far

    tanU*cscU - tanU*sinU

    (sinU/cosU)*(1/sinU) - (sinU/cosU)*sinU

    (1/cosU) - (sin^2U/cosU)

    (1-sin^2(U)/cosU)

    Half Angles Formula
    (1-1+cos(2U))/2cosU

    cos(2U)/2cosU

    Double angles Formula
    (2cos^2(U)-1)/2cosU

    cosU-1

    cosU-1 =/= cosU


    ands so i end up with that pesky -1 out there.

    so what am i doing wrong?
    For your last step:

    \frac{2\cos^2(U)-1}{2\cos(U)} \neq \cos(U)-1

    \frac{2\cos^2(U)-1}{2\cos(U)} = \frac{\cos^2(U)-1}{\cos(U)}

    You could do two things now. You can split the fraction:

    = \frac{\cos^2(U)}{\cos(U)} - \frac{1}{\cos(U)} = \cos(U) - \sec(U)

    Or you could use the trigonometric identity \sin^2x+\cos^2x=1

    \frac{\cos^2(U)-1}{\cos(U)} = \frac{-\sin^2x}{\cos(U)} = -\sin{x} \tan{x}

    I don't know why you want the answer to be cos(U). Is that the answer in your book?

    I think that last step should give you \cos(U) - \sec(U) or -\sin{x} \tan{x}, which are both the same thing.

    Hope that helps

    Mathemagister
    Last edited by mathemagister; April 9th 2010 at 09:25 AM.
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  3. #3
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    yes the cos(U) is part of the original question, we have to establish the identities by making both sides equal.

    this is a test which two people in the entire class passed, so the teacher is letting us redo it at home for partial credit and i just cant figure this stuff out.

    it was a 26 question test which we had an hour and a half to do. this is number 1. so I'll probably be back with more questions as i go through it
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