I have not watched the documentary you are referring to but in general there are several pieces of evidence that can be used to infer things like this.
In particular, scientists can try to infer the possible behaviors of extinct animals from living relatives. For instance, in other species (in [this case dinosaurs](https://www.cbsnews.com/colorado/news/markings-on-rocks-in-colorado-a-likely-sign-of-dinosaur-mating-behavior/)), there are fossilized remains of footprints showing long grooves or scrapes. In that case, they resemble what would be produced by the scuffing produced by birds engaged in the same mating rituals and fighting today — so it seems likely that the T. rexes were doing something similar.
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