So I'm going to start my undergrad degree in applied physics this summer, and I'm having a particularly annoying case of math envy. I decided to brush up on my physics and math skills before I go to uni, but this made me realize that I'm actually very bad at proving math theorems and the like. For example, trigonometric formulas. In high school I learned that sin(s+t)=sin(s)*cos(t)+cos(s)*sin(t), but never learned what the proof for this was. It's much easier to remember something when you can prove it, because then you only need to remember the basic rules (which you most likely already know). However, looking at the proof of this formula made me think "wait, what? I could never come up with this kind of proof on my own!" Thus, math envy. Now of course I'm not even in college yet, but has anyone else who went into physics or math experienced a similar thing? Is it normal to not be able to come up with all these proofs for such formulas by yourself at this time? Thanks.