Nope. I mean it is safe to take them together. Like, if it's a very mild pain, sure, take just one. Especially if you have a sensitive stomach. (Ibuprofen, with food and water, for pain + inflammation. Acetaminophen for anything else.) But if it's already pretty bad? Take the recommended dose for both at the same time. (With food and water. And NAC and a multivitamin if you have them.)
Acetaminophen can safely be mixed with Ibuprofen (OR naproxen OR aspirin.) - check stuff like cold and flu meds because they often already have one of those mixed in and you don't want to double up the wrong ones.
Ibuprofen, aspirin, and naproxen all work directly on the site of the pain itself and can be dangerous when mixed together. But they also reduce inflammation effectively as a result. Acetaminophen actually affects how your *brain* perceives pain signals - making you less sensitive to them. (Weirdly, this means that some studies have shown that acetaminophen can also temporarily reduce feelings of emotional pain and empathy???? Brains are weird.) Because these mechanisms are so different, you can layer them and get a boosted effect.
Remember- pain is bad for the body. Once you know the cause of the pain, it isn't doing you any more good, and it in fact is bad for you. Do what you need to do (safely) to get rid of pain.