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I have an expression with thousands of terms each of them has the form (1- Exp[-2 a x]) . I want to be able to write it as 2 Exp[- a x] Sinh[ a x] . How do I do this without doing it for each term separately and that too - by hand?

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Try rule Exp[- 2 z_] -> 1 - 2 Exp[-z ] Sinh[z ]

1 - Exp[-2 a x] /. Exp[- 2 z_] -> 1 - 2 Exp[-z ] Sinh[z ]
(*2 E^(-a x) Sinh[a x]*)
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