Problem

Source: Moldova TST Problem 5

Tags: trigonometry, Trigonometric inequality, algebra, inequalities, function



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