There’s a whole pile of math like this that kind of lies in this nether land between more advanced than you’ll get in most high school math¹ but less advanced than you’ll get in most college high school math that I was only ever exposed to when I took the classes for my teaching credential. One of my favorite was how cos/sin, tan/cot and sec/csc all can be derived from right triangles on a unit circle with the first…
The inequality stuff is just typical math olympiad material. Needed for solving olympiad problems, but doesn't matter that much for your overall math education from college and beyond.