Here’s the thing, if he/she does have something to hide you have to do it behind their back.
Another point, people before they cheat and people while they are cheating have the same “symptoms.” Like @jonsblond mentioned a woman usually knows, probably a man does to. When someone begins to be emotionally absent from a relationships the partner perceives the distance. Let’s just say it is the man in this example. He begins to be shorter tempered, the wife feels like she can’t do anything right and the man is overcritical. He might be less interested in sex. He is annoyed when his wife requests he does things. He might be coming home later, because he is not having a good experience at home. He may want more privacy and less questions in general. This guy might be moving away from the relationship and more open to affair, OR he might already be having an affair, it could be either. If the woman has been cheated on before by her husband or someone in the past she is very in tune with these symptoms, and even if the guy has done nothing outside of the marriage, she might feel compelled to check. He might be upset at the mistrust, because he has done nothing, nothing yet; but really they need to talk about what is wrong in the relationship. Sometimes these things pass, every relationship has tough spots, and may not need a big therapy session, but when things are tense in a relationship it would be wrong to deny it.
I am not talking about crazy jealous possessive controlling macho men or jealous neurotic women, that is a whole different thing that would drive me ‘round the bend. But, normal people who go through ups and downs in relationships.