Is it illegal to put a hidden camera in someone’s home if you want to catch a sexual abuse? The victim and the rapist don't know they are being filmed.

What the law says might depend on where they are.

How are you getting into their home? That would be trespassing in any state.

The court might rule the film inadmissable (in court) if it was obtained illegally.

Different areas, different rules, but even if the evidence is not allowed in court, it is still probable cause to start or expand an investigation. So far as I know, video can be used in court if audio is not there.

The main concern would be if access to the home had been allowed, or if it was an illegal entry. That would be a problem.

It must be assumed that it is illegal. Otherwise, it’s a violation of people’s privacy.

Generally yes – It’s illegal for an outsider to enter anyone’s home and plant a concealed recording device without a warrant or court order. At the very least it would be considered trespassing, and beyond that it can be seen as a violation of protections in the Civil Rights Act, punishable under federal law.

Your question as posted really lacks enough facts and specifics to determine whether there are any circumstances beyond personal suspicion or assumptions that could justify doing what you suggest. Rape and sexual abuse are serious crimes, but so is invading someone’s home without verifiable good cause.

If it isn’t your house, it’s definitiely illegal.

If it is your house, it’s shaky. Especially if the two people are over 18.