VMO 1983 Problem 2
(1) Show that (sin x + cos x) √2 ≥ 2 sin(2x) for all 0 ≤ x ≤ π/2. (2) Find all x such that 0 < x < π and 1 + 2 cot(2x)/cot x ≥ tan(2x)/tan x.
Community text Kalva (prase.cz mirror). Quoted with source.
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