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Homework Help: PROVing trigonometry indenties

  1. Sep 26, 2010 #1
    1. The problem statement, all variables and given/known data
    (tanx - cosecx)2 - (cotx - secx)2 = 2(cosecx - secx)


    2. Relevant equations
    tanx = sinx/cosx
    cotx = 1/tanx = cosx/sinx
    cosecx = 1/sinx
    secx = 1/cosx

    3. The attempt at a solution

    LHS = (tanx-cosecx)(tanx-cosecx) - (cotx-secx)(cotx-secx)
    = tan2x - tanxcosecx - tanxcosecx + cosec2x - cot2x + cotxsecx + cotxsecx
    = sin2x/cos2x - (sinx/cosx)(1/sinx) - (sinx/cosx)(1/sinx) + 1/sin2x - cos2x/sin2x + (cosx/sinx)(1/cosx) + (cosx/sinx)(1/cosx) - (1/cos2x)
    = sin2x/cos2x - 2sinx/sinxcosx + 1/sin2x - cos2x/sin2x + 2cosx/sinxcosx - 1/cos2x
    = sin2x-1 / cos2x + 1 - cos2x / sin2x - 2sinx+2cosx/sinxcosx
    = -1 + 1 - 2sinx+2cosx / sinxcosx
    = 2sinx + 2cosx / sinxcosx

    and i'm stucked
    help thanks in advance :)
    ps. if i post in the wrong place im sry cos im new :/
     
  2. jcsd
  3. Sep 26, 2010 #2

    fzero

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    Science Advisor
    Homework Helper
    Gold Member

    You need to use parentheses to clarify addition vs division to avoid making trivial mistakes. You missed a minus sign that's present in the part I bolded. With the correct signs in the last line, you can divide through to obtain the desired result.
     
  4. Sep 26, 2010 #3
    oh! thanks for pointing out my mistake , i've got the answer already :D thanks
     
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