The problem is that the foundation for trigonometry is rooted in the Pythagorean Theorem and that any proof would seemingly be based on circular reasoning. Mathematicians thought any proof based on trigonometry was impossible, but the two High School students provided a proof.
The proof was annotated in a posting by Wolfram Alpha developer @Shenghui Yang. See New trigonometric proof of Pythagorean theorem via law of sines posted in the Wolfram Community discussions about a year ago.
