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Inverse hyperbolic cosecant

The inverse hyperbolic cosecant can be expresses with logarithms as

 

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Explanation

We start with the hyperbolic cosecant

Substitution of e^θ = k gives

We continue only with the positive solution and substitute k = e^θ so that

Daarna nemen we de logaritmen

After substitution of θ = arcsch x we get

 

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