Difference between revisions of "1965 IMO Problems/Problem 1"
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Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality | Determine all values <math>x</math> in the interval <math>0\leq x\leq 2\pi </math> which satisfy the inequality | ||
<cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.</cmath> | <cmath>2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.</cmath> | ||
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== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
Revision as of 10:42, 16 July 2009
Problem
Determine all values 
in the interval 
which satisfy the inequality
![\[2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.\]](http://latex.artofproblemsolving.com/4/b/8/4b8f8dde7d81edc16f593f80f05d7d1b85bf26e0.png)
Solution
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