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- Thread starter Clara Chung
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Mark44

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From this page, https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions, I see that ##\sinh(\cosh^{-1}(x) = \sqrt{x^2 - 1}##, for |x| > 1.## Homework Statement

View attachment 214910

## Homework Equations

## The Attempt at a Solution

The attempt is in the picture. Is this the right method? Is there any faster method without cumbersome calculations?

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Thank you. I get the answer.From this page, https://en.wikipedia.org/wiki/Inverse_hyperbolic_functions, I see that ##\sinh(\cosh^{-1}(x) = \sqrt{x^2 - 1}##, for |x| > 1.

x=sinh(-arccosh(x+2))

=-sinh(arccosh(x+2))

=-root(x^2+4x+3)

And the website is very helpful

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So it is x^2=x^2+4x+3

X=-3/4

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