On my phone at a restaurant right now so I'm not looking it up but this was previously in a published paper in 2009. Not to rain on their parade: this is a great start for a couple of math prodigies, but they didn't quite discover a new proof.
On the Possibility of Trigonometric Proofs of the Pythagorean Theorem
Jason Zimba
Abstract. The identity cos2 x + sin2 x = 1 can be derived independently of the Pythagorean theorem, despite common beliefs to the contrary.