Read the textbook carefully, listen to the teacher, do the exercises carefully, and find them yourself. This statement seems to be nonsense, but it is actually the truth. With a solid foundation, you may have problems that you can't do. Looking at this long speech, I don't know what to say I believe that everyone has had such an experience. How can we avoid it?

Let's get one thing straight. What we have learned is very, very limited. The disadvantage is that this knowledge becomes very boring in the process of repetition, and it is difficult to arouse your interest in mathematics; The advantage is that limited knowledge means limited methods to solve problems. When solving a problem, master the general method and the problem will be solved easily.

For example, trigonometric function, your tool is nothing more than sine and cosine theorem of sine and cosine tangent and sum and difference of two angles, as simple as that! As for the inductive formula and the double-angle formula, they are essentially the same as the sum and difference formula of two angles; Every exam is definitely a time to push back the half-angle formula. In this way, as soon as you see the simplified requirements, you should first remove the redundant items, and then see if the current formula is like the sum and difference formula of two angles, which is definitely right, otherwise you will be wrong. As soon as I see conditions or problems with side length, I think of sine and cosine theorems. There is only a little regularity, don't be fooled by the title.