$\eqalign{
& \cos i: \cr
& {\sin ^{20}}x + \underbrace {{1 \over {1024}} + ... + {1 \over {1024}}}_{9\;so} \ge 10\root {10} \of {{{{{\sin }^{20}}x} \over {{{1024}^9}}}} = {{5{{\sin }^2}x} \over {256}} \cr
& \to {\sin ^{20}}x \ge {{5{{\sin }^2}x} \over {256}} - {9 \over {1024}} \cr
& tuong\;tu \cr
& {\cos ^{20}}x \ge {{5{{\cos }^2}x} \over {256}} - {9 \over {1024}} \cr
& \to {\sin ^{20}}x + {\cos ^{20}}x \ge {{5\left( {{{\sin }^2}x + {{\cos }^2}x} \right)} \over {256}} - {{18} \over {1024}} = {1 \over {512}} \cr
& dau = \leftrightarrow \sin x = \cos x = {{\sqrt 2 } \over 2} \cr} $