Formation of mathematical literacy, research, and creative competence in students is one of the main goals of mathematics education. One way to develop creative thinking skills among students is through teaching them how to solve challenging and non-standard problems, achieved through the mastery and diligence of the teacher. Non-standard transcendental problems, as well as problems solved using non-traditional methods, are often encountered in competitive and Olympiad tasks. The article considers the solution of non-standard transcendental equations using new strategic methods that go beyond traditional ones.Methods such as utilizing monotonicity, boundedness, function parity, domain of admissible values, multiplying equations by functions, and exploring numerical intervals are considered. Their application and effectiveness are demonstrated through examples. It is impossible to consider all methods for solving non-standard equations. Solving non-standard transcendental equations using the examples considered promotes students' creative understanding of the material they have learned and the development of their thinking. By using such examples in math clubs, extracurricular activities, olympiad preparation, as well as in final review sessions, students are engaged in finding effective methods for solving non-standard equations using non-traditional approaches. The work opens up new perspectives, offering a unique approach to solving equations in a modern context, and inspires students to take a creative approach to mathematics.