`tanh^-1 x = 1/2 ln((1+x)/(1-x)) , -1 < x < 1` Prove

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Given to prove

`tanh^(-1) x =1/2 ln((1+x)/(1-x))`

so let

`tanh^(-1) x =y`

=> `x= tanh(y)`

       `x =(e^y - e^-y)/(e^y + e^-y)`

=> `(e^y + e^-y)*x = (e^y - e^-y )`

=> `xe^y...

(The entire section contains 123 words.)

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