..just wanted to make sure im reading this right..
Sep 20, 2005 #3 dextercioby Science Advisor Homework Helper Insights Author 13,170 741 Here's the proof [tex] \tanh ix=\frac{\sinh ix}{\cosh ix}=\frac{i\sin x}{\cos x}=i\tan x [/tex] Therefore [tex] ix=\mbox{arc}\tanh \left(i\tan x\right) [/tex] Pick [itex] x=\arctan y [/itex] So [tex] i\arctan y=\mbox{arc}\tanh \left(i\tan\left(\arctan y\right)\right)=\mbox{arc}\tanh iy [/tex] q.e.d. Daniel.
Here's the proof [tex] \tanh ix=\frac{\sinh ix}{\cosh ix}=\frac{i\sin x}{\cos x}=i\tan x [/tex] Therefore [tex] ix=\mbox{arc}\tanh \left(i\tan x\right) [/tex] Pick [itex] x=\arctan y [/itex] So [tex] i\arctan y=\mbox{arc}\tanh \left(i\tan\left(\arctan y\right)\right)=\mbox{arc}\tanh iy [/tex] q.e.d. Daniel.