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Differentiating :calculus theory

  1. Dec 7, 2011 #1
    1. The problem statement, all variables and given/known data


    Verify the identity:

    arctanx + arctan(1/x)=∏/2

    using calculus theory.
    (Hint: Differentiate the left hand side of the identity)

    2. Relevant equations

    ?

    3. The attempt at a solution
    is this correct?

    tan(arctanx + arctan(1/x))
    = [tan(arctan(x)) + tan(arctan(1/x))][1 - tan(arctan(x))*tan(arctan(1/x))]

    = [x + 1/x]/[1 - x*1/x] = (x + 1/x)/0 = oo

    tan pi/2 = oo
     
  2. jcsd
  3. Dec 7, 2011 #2
    mmm.... they wanted you to do this:
    [tex]\frac{1}{1+x^2}+ etc....[/tex]
     
  4. Dec 7, 2011 #3
    where did that come from I'm confused??
     
  5. Dec 7, 2011 #4

    Mark44

    Staff: Mentor

    Start by using the hint, which is to differentiate the left side.
     
  6. Dec 7, 2011 #5
    f'(x)=1/(1+x2) + -1/(x2+1) =0

    for all x≠0

    function is constant on domain

    is this right?
     
  7. Dec 7, 2011 #6

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Yes, it is. I guessing they meant to specify x>0. Now just pick a nice value of x to put in to figure out what the constant is.
     
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