Taking a clue from the identity for the tangent of the sum of three angles, we form a corresponding functional equation in three variables. Assuming the function to be differentiable, we solve the functional equation and conclude that the solution is essentially the tangent function up to a constant multiple of the argument variable and a translation. This article involves trigonometry, multivariable calculus, differential equation and functional equation. The concept and methodology used can be understood by a student with a good background in multivariable calculus and differential equation. Teachers may also use this to stimulate further interest in students while teaching multivariate calculus and differential equation.

trigonometric identity, tangent function, functional equation, differential equation.

Received: October 5, 2023;  Accepted: November 3, 2023; Published: November 15, 2023

How to cite this article: Hang Su and Ramesh Sharma, Tangent function as a solution of a 3-dimensional functional equation, Far East Journal of Mathematical Education 25 (2023), 57-61. http://dx.doi.org/10.17654/0973563123016

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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