'cough-inducing' originates from English, specifically a compound of 'cough' and the present participle form of 'induce'. 'cough' comes from Old English 'cohh' (a word for the act of expelling air audibly), and 'induce' comes from Latin 'inducere', where 'in-' meant 'into' and 'ducere' meant 'to lead'.

'cough' changed from Old English 'cohh' and Middle English forms such as 'coughen' into the modern noun 'cough', while Latin 'inducere' passed into Old French as 'induire' and then into Middle and Modern English as 'induce' (giving the participle 'inducing'); the modern English compound 'cough-inducing' is formed from these elements.

Initially each element referred to 'an audible expulsion of air' (cough) and 'to lead into' (induce); together, in modern usage they evolved into the adjectival sense 'causing coughing' or 'likely to provoke a cough'.