Hyperbolic function proof

  • Thread starter Pietair
  • Start date
  • #1
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Homework Statement


Prove that:
(1+tanhx)/(1-tanhx)=e^(2x)

Homework Equations



09368019eae4f200d4ed8e266bfa50dc.png


The Attempt at a Solution



I tried substituting tanhx for (e^x-e^(-x))/(e^x+e^(-x)) and for (e^(2x)-1)/(e^(2x)+1))

But I really have no clue how to continue...
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
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Hi Pietair! :smile:

Hint : (1+tanhx)/(1-tanhx) = (1 + sinhx/coshx)/(1 - sinhx/coshx) = … ? :wink:
 
  • #3
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Thanks for your answer but it still doesn't make sense.

I don't know how to rewrite it to something more "common".
 
  • #4
tiny-tim
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Thanks for your answer but it still doesn't make sense.

I don't know how to rewrite it to something more "common".

try simplifying (1 + sinhx/coshx)/(1 - sinhx/coshx) …

get rid of the internal fractions :wink:
 
  • #5
59
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(coshx+sinhx)/(coshx-sinhx)

= (0.5e^x+0.5e^(-x)+0.5e^x-0.5e^(-x))/((0.5e^x+0.5e^(-x)-0.5e^x+0.5e^(-x))

= e^x/e^(-x)

= e^2x (proven)

Thanks a lot!
 

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