1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    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


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook