When do I use “can” & “could”?
In a company, the HR asked me:
"Could you please sign here".
I want to know whether it is correct or "Can " should be used or simply "Please sign here" is sufficient.
When to ideally use Could.
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Strictly logically speaking, asking "Can you sign here?" would be sufficiently answered by "yes" with no further action required. "Yes, I am able to." However, we generally understand that as a request in English, so we'll say "Yes" and sign. (I think in Russian, it's more common to use the imperative: "Sign here, please", and if you say "Can you sign here?" they'll say "of course" in a surprised way, but then do it anyway).
Anyway, saying "Could you please sign here?" instead is just a way to make the sentence more polite by making it less direct. The same happens in French - instead of saying "I want a cheese sandwich" at a restaurant (je veux), you say "I would like a cheese sandwich" (je voudrais) - again using the conditional, similar to English.
So, both are socially correct, the latter is more polite, and technically speaking you can say "Yes," do nothing, and look like a douche.