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Bosnia and Herzegovina TST 2004 Day 2 Problem 2

Source: Bosnia and Herzegovina Team Selection Test 2004

September 17, 2018

Inequalitycosinesinealgebra

Problem Statement

For

0 \leq x < \frac{\pi}{2}

prove the inequality:

a^2\tan(x)\cdot(\cos(x))^{\frac{1}{3}}+b^2\sin{x}\geq 2xab

where

a

and

b

are real numbers.