The purpose of this paper is to examine the possibility of the teaching via problem solving in high school mathematics. In this paper, we focused on the learning of the "addition theorems of trigonometric functions" in MAHTEMATICS II, and following was examined. 1) Through quantitative and qualitative investigations, the actual conditions of the activities of the students who worked on the theorems for the first time. 2) Through teaching practice, the effect and validity of the hypothetical ways of support based on the investigations. As a result, it has been understood that the hypothetical ways of support set in this paper worked effectively in the following three points: to understand the problem, to devise the plan for solving in the classroom, and to understand the proof method or meanings of the addition theorems of trigonometric functions. In a word, it is the main result of this paper to have suggested the possibility and the effectiveness of the teaching via problem solving in high school mathematics.
