..just wanted to make sure im reading this right..
Related Introductory Physics Homework Help News on Phys.org New technique builds super-hard metals from nanoparticles Wet and wild: There's lots of water in the world's most explosive volcano How did forelimb function change as vertebrates acquired limbs and moved onto land?
Related Introductory Physics Homework Help News on Phys.org New technique builds super-hard metals from nanoparticles Wet and wild: There's lots of water in the world's most explosive volcano How did forelimb function change as vertebrates acquired limbs and moved onto land?
Sep 20, 2005 #3 dextercioby Science Advisor Homework Helper Insights Author 13,017 566 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.