John D. Cook 3/10/2026

sinh( arccosh(x) )

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This technical article investigates the unexpected behavior of Mathematica when simplifying expressions like sinh(arccosh(x)). It explains that the simplification to √(x² − 1) is not universally valid due to the branch cut in the definition of arccosh. The post delves into complex analysis, discussing how arccosh is defined for real and complex arguments and why software must handle these edge cases carefully.

sinh( arccosh(x) )

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