IMO Shortlist 1967 problem 3


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Prove the trigonometric inequality \displaystyle \cos x < 1 - \frac{x^2}{2} + \frac{x^4}{16}, when \displaystyle x \in \left(0, \frac{\pi}{2} \right)\text{.}
Source: Međunarodna matematička olimpijada, shortlist 1967