- #1
Pole
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Homework Statement
Prove that (for every x smaller than -1)
[itex]\displaystyle \frac{1}{2}arctan\frac{2x}{1-x^{2}}+arccotx=\pi[/itex]
Homework Equations
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!