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8:03 AM
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Q: Proving $\sinh^{-1}x=-i\sin^{-1}ix$

Math GuyI discovered this relation while playing around with $\int\frac{\mathrm dx}{\sqrt{x^2+1}}$. Method 1: This is a standard integral, so it can be directly written as: $$\int\frac{\mathrm dx}{\sqrt{x^2+1}}=\sinh^{-1}x+C$$ Method 2: The integrand can be rewritten in the form $\frac1{\sqrt{1-t^2}}$ if...

In mathematics, the inverse hyperbolic functions are inverses of the hyperbolic functions, analogous to the inverse circular functions. There are six in common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse hyperbolic cotangent. They are commonly denoted by the symbols for the hyperbolic functions, prefixed with arc- or ar-. For a given value of a hyperbolic function, the inverse hyperbolic function provides the corresponding hyperbolic angle measure, for example arsinh...
8:28 AM
I see that on this particular question, the tag was added, removed and added back: math.stackexchange.com/posts/4974469/revisions

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