Difference between revisions of "1989 OIM Problems/Problem 2"
| (3 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
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) | + | <cmath>\frac{\pi}{2}+2sin(x)cos(y)+2sin(y)cos(z) > sin(2x)+sin(2y)+sin(2z)</cmath> |
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
| Line 7: | Line 7: | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe4.htm | ||
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
