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第二十九届国际数学奥林匹克竞赛有一道非常难的预选题: 命题 设a_i>0,β_i>0(1≤n,n>1),且sum from i=1 to n a_i=sum from i=1 to n β_i=π. 证明:sum from i=1 to n cosβ_i/sina_i≤sum from i=1 to n ctga_i (1) （蒙古提供)
The twenty-ninth International Mathematical Olympiad Olympiad has a very difficult pre-selection question: Propositions set a_i>0, β_i>0 (1≤n, n>1), and sum from i=1 to n a_i=sum from i= 1 to n β_i=π. Proof: sum from i=1 to n cosβ_i/sina_i≤sum from i=1 to n ctga_i (1) (provided by Mongolia)