What did the Triceratops use their horns for?

Context: There has been much speculation over the functions of Triceratops' head adornments. The two main theories have revolved around use in combat and in courtship display, with the latter now thought to be the most likely primary function.

Early on, Lull postulated that the frills may have served as anchor points for the jaw muscles to aid chewing by allowing increased size and thus power for the muscles. This has been put forward by other authors over the years, but later studies do not find evidence of large muscle attachments on the frill bones.

Triceratops were long thought to have used their horns and frills in combat with predators such as Tyrannosaurus, the idea being discussed first by Charles H. Sternberg in 1917 and 70 years later by Robert Bakker. There is evidence that Tyrannosaurus did have aggressive head-on encounters with Triceratops, based on partially healed tyrannosaur tooth marks on a Triceratops brow horn and squamosal; the bitten horn is also broken, with new bone growth after the break. Which animal was the aggressor is not known. Paleontologist Peter Dodson estimates that in a battle against a bull Triceratops, the Triceratops had the upper hand and would successfully defend itself by inflicting fatal wounds to the Tyrannosaurus using its sharp horns. Tyrannosaurus is also known to have fed on Triceratops, as shown by a heavily tooth-scored Triceratops ilium and sacrum.

Answer: The Triceratops used their horns for both courtship and combat, including defending against aggressive predators such as the Tyrannosaurus.