The police arrest you and bring you in for questioning. They tell you that you have a right to remain silent, but you decide to answer some questions.
While they interrogate you, are the police held to any standards regarding telling the truth? Or are they allowed to lie to you whenever they want?
There are standards that have to be used during an interrogation. Police are never allowed to use physical coercive tactics. In layman's terms, they can't torture you. They can't send in a physically imposing officer who says he's going to beat you up if you don't tell the truth, even though you see these types of tactics in movies and TV shows. They're illegal and a confession obtained this way isn't going to stand up. Police also cannot drug you or do anything else that is considered inhumane.
All that being said, they absolutely can lie. That's not considered inhumane and they're allowed to do it intentionally.
For instance, if they arrested you with someone else, they could come in and tell you that the other person already confessed in a different room. They could say they know you're guilty based off of that confession. They're just trying to trick you into confessing, even though the other person said nothing at all. They're allowed to do it. If it happens, there's a good chance they're doing it to both of you, in separate rooms, at the same time.
This is why it's incredibly important to know all of your rights, including the right to an attorney, if you're ever arrested.
Source: FindLaw, "FAQs: Police Interrogations," accessed Nov. 17, 2017