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Trying to prove a trig identity

  1. May 31, 2009 #1
    1. The problem statement, all variables and given/known data

    cos^2x-cotx
    --------------- = cot^2x
    sin^2x-tanx

    2. Relevant equations



    3. The attempt at a solution

    every solution I get gives me a zero, not cot^2
     
  2. jcsd
  3. May 31, 2009 #2

    tiny-tim

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    Welcome to PF!

    Hi james_stewart! Welcome to PF! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Either write cot= cos/sin, tan = sin/cos,

    or just multiply both sides by sin2x-tanx :wink:
     
  4. May 31, 2009 #3
    i did and i'm not getting the proper results.

    when i convert cot and tan to cos/sin and sin/cos i get

    cos^2-cos^2
    -------------
    sin^2-sin^2
     
  5. May 31, 2009 #4

    tiny-tim

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    (please use the X2 tag just above the Reply box)
    No, you should get cos2 - cos/sin on the top …
     
  6. May 31, 2009 #5
    i did

    and on the bottom i get sin2-sin/cos
     
  7. May 31, 2009 #6

    tiny-tim

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    ok, now put sin2-sin/cos as one fraction (ie with everything over the same denominator), and the same for cos2-cos/sin
     
  8. May 31, 2009 #7
    That's how i did it. but where do i get cot2 from this?

    cos2 - cos/sin
    --------------
    sin2 - sin/cos
     
  9. Jun 1, 2009 #8

    tiny-tim

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    erm :redface: … put sin2 - sin/cos as one fraction (ie with everything over the same denominator), and the same for cos2 - cos/sin
     
  10. Jun 1, 2009 #9

    rl.bhat

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    You can write numerator as
    [cos2xsinx -cosx]/sinx. Then take cos(x) common.
    Repeat the same thing for denominator and simplify.
     
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