In this paper, we provide alternative proofs to some results proposed in the article "New inequalities involving circular, inverse circular, hyperbolic, inverse hyperbolic and exponential functions" authored by Yogesh J. Bagul.
The main objective of this paper is to establish several new lower and upper bounds for the functions sinh x/x and cosh x. Following the simple approach, our results give refinements and generalizations of some known inequalities involving these functions.
The aim of this paper is to present new, simple and sufficiently sharp bounds for arcsine and arctangent functions. Some of the bounds are computationally efficient while others are efficient to approximate the integrals Int_{a}^{b} (arcsin x)/x dx and Int_{a}^{b} (arctan x)/x dx. As a matter of interest, several other sharp and generalized inequalities for (arcsin x)/x and (arctan x)/x are also established which are efficient to give some known and other trigonometric inequalities
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