Difference between revisions of "1989 OIM Problems/Problem 2"
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Let <math>x</math>, <math>y</math>, <math>z</math> three real numbers such that <math>0<x<y<z<\frac{\pi}{2}</math>. Prove the following inequality: | Let <math>x</math>, <math>y</math>, <math>z</math> three real numbers such that <math>0<x<y<z<\frac{\pi}{2}</math>. Prove the following inequality: | ||
<cmath>\frac{\pi}{2}+2sin(x)cos(y)+2sin(y)cos(z) > sin(2x)+sin(2y)+sin(2z)</cmath> | <cmath>\frac{\pi}{2}+2sin(x)cos(y)+2sin(y)cos(z) > sin(2x)+sin(2y)+sin(2z)</cmath> | ||
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~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Latest revision as of 12:30, 13 December 2023
Problem
Let 
, 
, 
three real numbers such that 
. Prove the following inequality:
![\[\frac{\pi}{2}+2sin(x)cos(y)+2sin(y)cos(z) > sin(2x)+sin(2y)+sin(2z)\]](http://latex.artofproblemsolving.com/2/a/5/2a5aec67265771ac0a20fd0736250785787e0584.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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