MathDB

trigonometry

Source: Ukraine 1997 grade 11

July 22, 2009

trigonometryalgebra unsolvedalgebra

Problem Statement

Prove that among any four distinct numbers from the interval

(0,\frac{\pi}{2})

there are two, say

x,y,

such that: 8 \cos x \cos y \cos (x\minus{}y)\plus{}1>4(\cos ^2 x\plus{}\cos ^2 y).