MathDB
Inequality

Source: 0

April 21, 2009
inequalitiestrigonometry

Problem Statement

If inequality \frac {\sin ^{3} x}{\cos x} \plus{} \frac {\cos ^{3} x}{\sin x} \ge k is hold for every x(0,π2) x\in \left(0,\frac {\pi }{2} \right), what is the largest possible value of k k?
<spanclass=latexbold>(A)</span> 12<spanclass=latexbold>(B)</span> 34<spanclass=latexbold>(C)</span> 1<spanclass=latexbold>(D)</span> 32<spanclass=latexbold>(E)</span> None<span class='latex-bold'>(A)</span>\ \frac {1}{2} \qquad<span class='latex-bold'>(B)</span>\ \frac {3}{4} \qquad<span class='latex-bold'>(C)</span>\ 1 \qquad<span class='latex-bold'>(D)</span>\ \frac {3}{2} \qquad<span class='latex-bold'>(E)</span>\ \text{None}