Ultimately, if you’re worried that your significant other is on a dating site, there are many options for sleuthing (ranging from a quick scan through emails and browser history to more intensive—and expensive—actions).
If nothing else works (or you don't have the time to conduct an exhaustive search that may or may not be conclusive), consider hiring a private invesitgator.
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If all else fails, you can hire a professional investigator to find out for certain whether your signifigant other is using a dating site.