They don’t, I’m afraid. Over the counter cough medicines you can buy in the US are no more effective than a placebo (a fake medicine).
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC65295/
>Over the counter cough medicines for acute cough cannot be recommended because there is no good evidence for their effectiveness.
I had a class in college where this was discussed. The professor said it’s literally just sticky syrup coating the back of your throat. This offers a short lived feeling of relief and gives you something to cough up instead of just continually irritating your throat with dry hacking. You can get a similar effect from candy, although for me the menthol seems to help a little. Also, let’s not knock the benefits of placebos. Sometimes ignorance is bliss.
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