Difference between revisions of "1965 IMO Problems/Problem 1"

(Created page with '== Problem == 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{…')
 
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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>
 
  
 
== Solution ==
 
== Solution ==
 
{{solution}}
 
{{solution}}

Revision as of 11:42, 16 July 2009

Problem

Determine all values $x$ in the interval $0\leq x\leq 2\pi$ which satisfy the inequality \[2\cos x \leq \left| \sqrt{1+\sin 2x} - \sqrt{1-\sin 2x } \right| \leq \sqrt{2}.\]

Solution

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