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can anyone simplify, $\sin^{-1}\tanh\theta=?$ in a better equation?

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i see no equation – Dominic Michaelis Mar 6 '13 at 9:30
I think, you missed an $=$-sign and something on the right hand side of the equation. – born Mar 6 '13 at 9:32
and i see an expression – Aang Mar 6 '13 at 9:32
@Dominic Michaelis can solve it $\sin^{-1}\tanh\theta=?$ – Neo Mar 6 '13 at 9:32
nope ? is not in the image of $\sin^{-1}$ i am afraid – Dominic Michaelis Mar 6 '13 at 9:33
up vote 3 down vote accepted

You are looking for the Gudermannian function. See Wikipedia or Mathworld.

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ok thank you. so $\sinh^{-1}\tan x$ is The inverse Gudermannian function, – Neo Mar 6 '13 at 13:07

$\sin^{-1}\tanh x=2{\tan^{-1} \tanh x} \cosh x \sqrt {\operatorname{sech}^2 x}$

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