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三角关系式(等式与不等式)之多令人眼花缭乱,寻觅它们之间的联系则是人们所探讨的问题之一。本文给出一个重要的三角变换,它既是建立三角关系式等价结构的基础,又是发现新的三角关系式的一个重要源泉。 角变换定理 如果由条件A+B+C=π独立地推出命题f(A,B,C)成立,那么相应地有命题f(A′,B′,C′)成立,其中 该定理可由A′+B′+C′=(k+1)π-k(A+B+C)=π得证。
Triangular relational equations (equals and inequalities) are dazzling, and finding the connection between them is one of the issues that people are discussing. This paper presents an important trigonometric transformation, which is both the basis for the establishment of a triangular relational equivalent structure and an important source for the discovery of new triangular relational expressions. If the theorem of angular transformation holds independently from the condition A + B + C = π, the proposition f(A, B, C) is established, then the corresponding proposition f(A’, B’, C’) holds, where the theorem can be defined by A The result of ’+B’+C’=(k+1)π-k(A+B+C)=π is proved.