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 one year ago
Does anyone know where you could find the deduction of the inverse of tanh(x) starting from the standard hyperbolic trigonometry definitions? (Or does anyone possibly know how to deduce it from them?)
 one year ago
Does anyone know where you could find the deduction of the inverse of tanh(x) starting from the standard hyperbolic trigonometry definitions? (Or does anyone possibly know how to deduce it from them?)

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Noliec
 one year ago
Best ResponseYou've already chosen the best response.2@hartnn , @TuringTest , @AravindG Please help ;_;

Noliec
 one year ago
Best ResponseYou've already chosen the best response.2I basically get it, down to tanh(x)=(e^(2x)1)/(e^(2x)+1)

Noliec
 one year ago
Best ResponseYou've already chosen the best response.2Indeed, but how do you go from here to the inverse of tanh(x)?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1do u know componendo  dividendo ?

AravindG
 one year ago
Best ResponseYou've already chosen the best response.0Take tanh x=y. Then apply log on both sides.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1if a/b = c/d then (a+b) /(ab) = (c+d)/ (cd) did u know this ?

Noliec
 one year ago
Best ResponseYou've already chosen the best response.2That's what I did, I didn't get anywhere on the log expression though. Hmm, not sure hartnn.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1that rule is called componendodividendo apply that for y/1= (e^(2x)1)/(e^(2x)+1)

Noliec
 one year ago
Best ResponseYou've already chosen the best response.2I'd have to give a proof in order to utilize it though. D: It's supposed to be solved without it.

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1that will isolate e^2x and hence you can apply log

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1lol ok, don't apply that rule (bdw, that was algebraic property) y= (e^(2x)1)/(e^(2x)+1) y (e^2x +1) = e^2x 1 y e^2x + y = e^2x 1 y e^2x e^2x = 1y need i go further ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1hint for next step factor out e^2x from on left side

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1but did u get what i did ?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1\(\huge \dfrac{1}{2}\ln (\dfrac{1+x}{1x})\) you should get this

hartnn
 one year ago
Best ResponseYou've already chosen the best response.11y / y1 = (1+y)/ (1y) the 1/2 will come outside ln right ? because 2x= ln (...)

Noliec
 one year ago
Best ResponseYou've already chosen the best response.2What happens after you apply ln?

hartnn
 one year ago
Best ResponseYou've already chosen the best response.1e^2x =[(1+y)/(1y) ] clear till here ??
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