The simplification of mathematical expressions with symbolic approaches

Simplification is one of the basic methods that transform mathematical expressions into simpler forms, making them easier to understand and manipulate. In this study, a simplification system (TrigonSimfier) is developed, which reduces trigonometric expressions to simpler forms. Complex expressions containing trigonometric functions such as sine, cosine, tangent, cotangent, secant, and cosecant are converted into an abstract syntax tree with an LL(k) parser created by JavaCC. The hierarchical structure of the tree enables expressions to be easily represented structurally and simplified effectively, using formal grammars and algorithms developed with the Visitor design pattern. TrigonSimfier makes significant contributions to symbolic computation processes in a wide range of applications, from educational tools to automatic reasoning systems. This new approach can provide a different perspective on the simplification of trigonometric expressions and provide a basis for future studies.