Information that you voluntarily disclose to a police officer (after you have been properly warned) is generally admissible at trial. The key word is "voluntary." Police officers are not allowed to use physical force or psychological coercion to get you to talk to them. The days of the rubber hose, protracted grilling under bright lights, and severe sleep deprivation are pretty much over. If police officers obtain information through any of these illegal means, the information cannot be used by the prosecutor at trial. In addition, under the rule known as "the fruit of the poisonous tree," any evidence that the police obtain as the result of a coerced statement is equally inadmissible.
Defendants often claim that police officers coerced them into talking. And it's just as common for police officers to say that the defendants spoke voluntarily. If the police physically coerce a defendant into talking, the defendant can support his coercion claims with photos of marks and bruises. But actual police brutality is unusual, and a defendant cannot usually offer independent evidence to support his claims of psychological coercion. Judges, believing that defendants have a greater motivation to lie than do police officers, usually side with the police and conclude that no coercion took place.