The history of mathematics is rigorous, so every theorem has been strictly proved. Let you deduce in order to cultivate your rigor and logical thinking, because it is not good to write it when you need to prove it in the future. You can't tell anyone I know, but you can't write it ... it's an exercise. There is also a self-derived formula, which is particularly easy to remember and not easy to forget. We should write down conclusions and use them frequently in exams, but we need to prove what we have found. For example, many questions in the back need to be guessed first and then proved. You are not familiar with derivation. How can you prove it? Every step has a reason.

I hope that when I encounter a theorem or formula, I can deduce it myself. Unless the teacher says that the proof process is beyond the scope of study, it is better to prove it yourself and ask the teacher to correct me.

If you remember, remember the conclusion. Theorem, in particular, can be used directly, as long as you indicate what theorem it is.

Axioms don't need proof, just remember.