Yes. Police can, will, and often do lie -- especially if it helps them make arrests. One obvious example of this is when undercover officers claim not to be police. The rules regarding entrapment usually tip in favor of law-enforcement, so police won't hesitate to trick you into incriminating yourself or others. This is particularly common during interrogations in which officers might tell you that "your friend already gave you up, so you might as well come clean."
The best defense against these manipulative tactics is to avoid saying anything to police without first speaking with an attorney.
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