IMO 1988 LL MON66

Suppose \alphai > 0, \betai > 0 for 1 \leqi \leqn (n > 1) and that

imolonglistmathematicsolympiad

IMO 1988 LL MON66

Origin: MON

Problem

Suppose \alphai > 0, \betai > 0 for 1 \leqi \leqn (n > 1) and that n i=1 \alphai = n i=1 \betai = \pi. Prove that n  i=1 cos \betai sin \alphai \leq n  i=1 cot \alphai.