Could somebody please prove these identities and explain a little bit ? I just can't figure them out.

sinh^-1x = ln(x + sq.rt of(x^2 + 1))

cosh^-1x = ln(x + sq.rt of (x^2 + 1))

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

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- Jun 21st 2006, 06:37 AMyakkowCan somebody prove - Hyperbolic functions
Could somebody please prove these identities and explain a little bit ? I just can't figure them out.

sinh^-1x = ln(x + sq.rt of(x^2 + 1))

cosh^-1x = ln(x + sq.rt of (x^2 + 1))

tanh^-1x = (1/2)ln ( (1+x)/(1 - x) ) - Jun 21st 2006, 06:53 AMThePerfectHackerQuote:

Originally Posted by**yakkow**

Since,

is a bijective function it has an inverse.

Thus you interchange the x and y in,

To get,

Thus,

Thus,

Thus,

Allow, thus,

Thus,

Thus,

Which is,

Since, we have,

Thus,

Thus,