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: Trigonometric proof using derivatives

  1. Jan 20, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that (for every x smaller than -1)
    [itex]\displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}+arccotx=\pi[/itex]

    2. Relevant equations

    3. The attempt at a solution
    So i split the formula into two parts:
    [itex]\displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}[/itex] and [itex]\displaystyle \pi-arccotx[/itex]
    Calculated their derivatives separately
    And they are both equal to [itex]\displaystyle \frac{1}{x^{2}+1}[/itex]

    And I'm wondering whether it's the end of the task or should I prove some other things, especially something connected to the main assumption of x<-1 or any other.

    Thanks in advance!
  2. jcsd
  3. Jan 20, 2012 #2
    If [itex]f^\prime=g^\prime[/itex], then this doesn't mean f=g necessarily. But it does mean that f=g+C with C a real constant/

    Note that the above only holds if the domain of f and g is an interval.
  4. Jan 21, 2012 #3
    Thank You, now I know that it isn't sufficient.
    But I can't really come up with a complete solution.
    What should I add ? So that the task would be marked well
    How to calculate the value of that constant?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook