New Inequalities of Cusa–Huygens Type - Ling Zhu (Mathematics, 2021)
Using the power series expansions of the functions <semantics>cotx,1/sinx</semantics> and <semantics>1/sin2x</semantics>, and the estimate of the ratio of two adjacent even-indexed Bernoulli numbers, we improve Cusa–Huygens inequality in two directions on <semantics><mfenced separators="" open="(" close=")">0,π/2</mfenced></semantics>. Our results are much better than those in the existing literature.