..just wanted to make sure im reading this right..
Related Introductory Physics Homework Help News on Phys.org Study verifies a missing piece to urban air quality puzzle Rough seas delay escape test for SpaceX crew capsule Male sparrows are less intimidated by the songs of aging rivals
Related Introductory Physics Homework Help News on Phys.org Study verifies a missing piece to urban air quality puzzle Rough seas delay escape test for SpaceX crew capsule Male sparrows are less intimidated by the songs of aging rivals
Sep 20, 2005 #3 dextercioby Science Advisor Homework Helper Insights Author 12,977 540 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.