IMO Shortlist 1965 problem 1
Dodao/la:
arhiva2. travnja 2012. Determine all values of
![x](/media/m/f/1/8/f185adeed9bd346bc960bca0147d7aae.png)
in the interval
![0 \leq x \leq 2\pi](/media/m/6/5/f/65fb0c1199920bbff9126f98c4e59ebe.png)
which satisfy the inequality
%V0
Determine all values of $x$ in the interval $0 \leq x \leq 2\pi$ which satisfy the inequality $$2 \cos{x} \leq \sqrt{1+\sin{2x}}-\sqrt{1-\sin{2x}} \leq \sqrt{2}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1965