An Optimal Inequality For The Tangent Function

TL;DR

This paper establishes optimal inequalities for the tangent function within the interval (-π/2, π/2), identifying the best possible exponents to make these inequalities tight.

Contribution

It introduces the first set of inequalities for tangent with proven optimal exponents, enhancing the understanding of tangent's bounds.

Findings

Derived inequalities with optimal exponents for tangent

Identified the best possible constants for these inequalities

Enhanced bounds for tangent function within the specified interval

Abstract

In this note we deal with some inequalities for the tangent function that are valid for $x$ in $(-\pi/2,\pi/2)$. These inequalities are optimal in the sense that the best values of the exponents involved are obtained.