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Sharp inequalities related to the Adamovic-Mitrinovic, Cusa, Wilker and Huygens results

Sharp inequalities related to the Adamovic-Mitrinovic, Cusa, Wilker and Huygens results

In this paper, we establish sharp inequalities for trigonometric functions. For example, we consider the Wilker inequality and prove that for 0 < x < ?/2 and n ? 1, 2 + (?n?1 j=2 dj+1x2j+ ?nx2n) x3 tan x < (sin x/x)2 + tan x/x < 2 + (?n?1 j=3 …