Home Competitions PE-MO 2014 Problem 1
Find all triples ( α , β , θ \alpha, \beta,\theta α , β , θ ( sin α + cos β + 1 ) 2 ≥ 2 ( sin α + 1 ) ( cos β + 1 ) (\sin \alpha + \cos \beta + 1)^2 \ge 2(\sin \alpha + 1)(\cos \beta + 1) ( sin α + cos β + 1 ) 2 ≥ 2 ( sin α + 1 ) ( cos β + 1 ) ( sin β + cos θ + 1 ) 2 ≥ 2 ( sin β + 1 ) ( cos θ + 1 ) (\sin \beta + \cos \theta + 1)^2 \ge 2(\sin \beta + 1)(\cos \theta + 1) ( sin β + cos θ + 1 ) 2 ≥ 2 ( sin β + 1 ) ( cos θ + 1 ) ( sin θ + cos α + 1 ) 2 ≥ 2 ( sin θ + 1 ) ( cos α + 1 ) . (\sin \theta + \cos \alpha + 1)^2 \ge 2(\sin \theta + 1)(\cos \alpha + 1). ( sin θ + cos α + 1 ) 2 ≥ 2 ( sin θ + 1 ) ( cos α + 1 ) .
Dataset text AI-MO AoPS . Quoted with source.
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