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Simple inequality involving sine function

Source: Moldova TST Problem 5

April 1, 2015
trigonometryTrigonometric inequalityalgebrainequalitiesfunction

Problem Statement

Let c∈(0,π2),a=(1sin(c))1cos2(c),b=(1cos(c))1sin2(c)c\in \Big(0,\dfrac{\pi}{2}\Big) , a = \Big(\dfrac{1}{sin(c)}\Big)^{\dfrac{1}{cos^2 (c)}}, b = \Big(\dfrac{1}{cos(c)}\Big)^{\dfrac{1}{sin^2 (c)}}. \\Prove that at least one of a,ba,b is bigger than 201511\sqrt[11]{2015}.
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