- #1

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## Homework Statement

Prove that:

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

## Homework Equations

## 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...

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- Thread starter Pietair
- Start date

- #1

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Prove that:

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

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...

- #2

tiny-tim

Science Advisor

Homework Helper

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Hi Pietair!

Hint : (1+tanhx)/(1-tanhx) = (1 + sinhx/coshx)/(1 - sinhx/coshx) = … ?

Hint : (1+tanhx)/(1-tanhx) = (1 + sinhx/coshx)/(1 - sinhx/coshx) = … ?

- #3

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

- #4

tiny-tim

Science Advisor

Homework Helper

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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

- #5

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= (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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