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For which $x$ does an inequality hold?

Source: Spanish Mathematical Olympiad 1965 P4

November 15, 2016
inequalities

Problem Statement

Find all the intervals II where any element of the interval x∈Ix \in I satisfies cos⁡x+sin⁡x>1.\cos x +\sin x >1. Do the same computation when xx satisfies cos⁡x+∣sin⁡x∣>1.\cos x +\vert \sin x \vert>1.
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