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Prove Identity

  1. Feb 13, 2009 #1
    1. The problem statement, all variables and given/known data

    tan^2x + cos2x =1 - cos2xtan^2x

    2. Relevant equations



    3. The attempt at a solution
    I have not really gotten anywhere.
     
  2. jcsd
  3. Feb 13, 2009 #2

    Dick

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    Use cos(2x)=cos(x)^2-sin(x)^2 and tan(x)=sin(x)/cos(x) to turn everything into sines and cosines. Then clear out the denominators and start rearranging things.
     
  4. Feb 13, 2009 #3
    I have gotten it to


    (sin(x)^2/cos(x)^2) + (cos(x)^2- sin(x)^2) = 1- (cos (x)^2 - sin(x)^2)(sin(x)^2/cos(x)^2)

    not sure how to proceed
     
  5. Feb 13, 2009 #4

    Dick

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    Good so far. Multiply out the right side and multiply both sides by cos(x)^2 to clear out the fractions. Does anything cancel? Rearrange what's left.
     
  6. Feb 13, 2009 #5
    Its just not happenin for me right now

    I have it at sin(x)^2 cos(x)^2(cos(x)^2 - sin(x)^2) = cos(x)^2 - (cos(x)^2- sin(x)^2) sin(x)^2
     
  7. Feb 13, 2009 #6
    I meant to put a + after the first sin(x)^2
     
  8. Feb 13, 2009 #7

    Dick

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    Just keep going. Multiply out the terms with parentheses.
     
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