Abstract
In this paper we, respectively, give simple proofs of some remarkable trigonometric inequalities, based on the Pade approximation method. We also obtain rational refinements of these inequalities. We are convinced that the Pade approximation method offers a general framework for solving many other similar inequalities.
Highlights
Introduction and motivationThe starting point of this paper is the following famous inequalities
The Wilker inequality asserts that sin x tan x + >
Was established by Adamović and Mitrinović. Another inequality which is of interest to us is the following: sin x + tan x > x for all x ∈
Summary
Introduction and motivationThe starting point of this paper is the following famous inequalities. The Wilker inequality asserts that sin x tan x + > Huygens inequality for sine and tangent functions states that for x sin x + tan x > x. ). Another inequality which is of interest to us is the following: sin x + tan x > x for all x ∈
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