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How to solve this inverse trigonometry question

  1. Feb 1, 2012 #1
    1. The problem statement, all variables and given/known data

    tan-1[2x/(1-x2)]+cot-1[(1-x2)/2x]=2π/3

    2. The attempt at a solution


    tan-1[2x/(1-x2)]+cot-1[(1-x2)/2x]=2π/3
    tan-1[2x/(1-x2)]=2π/6
    take tan on both sides
    2x/(1-x2) =sqrt(3)
    quadratic equation so it should have 2 solutions(sqrt(3) and sqrt(1/3)).But this question has four solution.. Where am i missing solutions. Can you please help me to figure out the error..
    thanks
    ---------------
    vikash
     
  2. jcsd
  3. Feb 1, 2012 #2

    eumyang

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    According to Wolframalpha, there are two solutions, 1/√3 and -√3. How do you know that there are four solutions?
     
  4. Feb 1, 2012 #3
    How did you get from the first line to the second?
     
  5. Feb 1, 2012 #4

    SammyS

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    cot-1(a/b) = tan-1(b/a)

    I.e.: cot(x) = 1/tan(x)
     
  6. Feb 2, 2012 #5
    Thanks for link.
    There are more two answers in book that's why i ask. But now they will be marked as wrong.
     
  7. Feb 2, 2012 #6
    Ah right, missed that. Thanks.
     
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