Cops are allowed to lie to you relentlessly. Even if they do something illegal like questioning you without reading you your rights, they know you’ll have to fight it in court. Things are stacked in their favor pretty strongly. Even if you end up fighting them in court over a Miranda violation, that’s a problem for the prosecutor, not the cop arresting you.

Be relentlessly polite to the cops while admitting nothing. They usually don’t deserve politeness but it lessen the chance of them harming you.