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Homework Help: Trig problem

  1. Jun 14, 2010 #1
    1. The problem statement, all variables and given/known data

    (Cos[x]^2) (Tan[x] + Cot[x]) Simplify the equation by hand!!

    2. Relevant equations



    3. The attempt at a solution

    cos^2 / (tan + cot)
    cos^2 / (sin/cos + cos/sin) * sin*cos/(sin*cos)
    sin*cos^3 / (sin^2 + cos^2)
    sin*cos^3 / 1
    sin(x) * cos^3(x)

    this is wrong b/c i divided it...

    NVM found the answer:

    (cos^2(x))(sin(x)/cos(x) + cos(x)/sin(x))
    cos(x)sin(x) + cos^3(x)/sin(x)
    cos(x)sin(x) + cos^2(x)cos(x)/sin(x)
    cos(x)sin(x) + (1 - sin^2(x))cos(x)/sin(x)
    cos(x)sin(x) + (cos(x) - sin^2(x)cos(x))/sin(x)
    cos(x)sin(x) + cot(x) - sin(x)cos(x)
    cot(x)
     
    Last edited: Jun 14, 2010
  2. jcsd
  3. Jun 14, 2010 #2

    Mentallic

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    Homework Helper

    Sorry, it's wrong because you divided what?

    [tex]\frac{cos^2x}{tanx+cotx}\equiv sinx. cos^3x[/tex]

    The question says simplify [tex]cos^2x(tanx+cotx)[/tex]. Was this a typo?
     
  4. Jun 14, 2010 #3

    Mentallic

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    It's hard to read what you've done... And I can tell you now that it's not equivalent to cot(x).
     
  5. Jun 15, 2010 #4
    I get cot(x) as well, though you can skip quite a few steps in the simplification.
    Graphing confirms these are equivalent.
     
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