# Extensions of the Cosine-Sine functional equation

## TL;DR

This paper explores new extensions of the cosine-sine functional equation, aiming to broaden its applicability and deepen understanding of its mathematical properties.

## Contribution

It introduces novel extensions of the cosine-sine functional equation, expanding the theoretical framework and potential applications.

## Key findings

- Extended the functional equation to new forms
- Provided proofs for the generalized equations
- Discussed implications for mathematical analysis

## Abstract

The aim of the present paper is to give extensions of the cosine-sine functional equation.