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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.

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    You could delete it, but it would be more helpful to at least write a sketch of what you did, so it can be checked for correctness.2012-09-06

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