Mathematics is considered a tool for many other subjects at all educational levels, and is also a subject with rich potential that can be exploited to develop students’ thinking. Many students, although ca-pable and have good qualities, lack creativity and do not try to find the connection between the hypothesis and the conclusion of the problem to form the best solution. Therefore, training the ability to analyze and change hypotheses and conclusions at the same time is an important issue in the process of developing learners’ thinking, contributing to the formation of intellectual qualities and effective logical arguments. Physical. In this article, through analyzing a number of problems using knowledge of trigonometry and inequalities, we aim to help learners develop analytical capacity, the ability to self-study, self-discover and solve problems.