Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would like to derive the following expression for inverse cotangent:

$\cot^{-1} (z) = \frac{i}{2}[\ln(\frac{z-i}{z}) - \ln(\frac{z+i}{z})]$

But I don't want to take it as "definition" as this page (http://mathworld.wolfram.com/InverseCotangent.html) seems to suggest that, that is the 'standard' defintion (or at least a practical one).

In essence, I'm looking for a definition which only relies on tangent, inverse tangent, and cotangent.

share|improve this question
    
I don't understand your requirement. In any event, would you allow the use of $$\cot\,z=i\frac{\exp(iz)+\exp(-iz)}{\exp(iz)-\exp(-iz)}$$ as a definition for cotangent? –  J. M. Sep 4 '12 at 1:33
    
seems valid....... so are you wanting me to apply the right hand sides and try to show that its z? –  Squirtle Sep 4 '12 at 1:39
    
I presume you know the usual procedure for inverting a function? –  J. M. Sep 4 '12 at 1:41
    
the inverse of a trig function isn't its reciporal .... so I'm not sure I know what you are suggesting. –  Squirtle Sep 4 '12 at 1:53
    
Would you know how to obtain $x=\pm\sqrt{y}$ from $y=x^2$? That's what I meant when I asked you if you know how to invert a function. –  J. M. Sep 4 '12 at 2:02

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.