# On generalization of D'Aurizio-S\'andor trigonometric inequalities with a parameter

## TL;DR

This paper generalizes the D'Aurizio-Sándor trigonometric inequalities using an elementary approach, providing alternative proofs and extending the inequalities to hyperbolic functions.

## Contribution

It introduces a new generalized form of the D'Aurizio-Sándor inequalities and extends their applicability to hyperbolic functions.

## Key findings

- New generalized inequalities for trigonometric functions
- Alternative proof of existing inequalities
- Extension to hyperbolic functions

## Abstract

In this work, we generalize the D'Aurizio-S\'andor inequalities (\cite{D'Aurizio,Sandor}) using an elementary approach. In particular, our approach provides an alternative proof of the D'Aurizio-S\'andor inequalities. Moreover, as an immediate consequence of the generalized D'Aurizio-S\'andor inequalities, we establish the D'Aurizio-S\'andor-type inequalities for hyperbolic functions.