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IMO LongList 1967, Poland 5

Source: IMO LongList 1967, Poland 5

December 16, 2004
trigonometryalgebraTriangleTrigonometric IdentitiesIMO ShortlistIMO Longlist

Problem Statement

Show that a triangle whose angles AA, BB, CC satisfy the equality sin⁡2A+sin⁡2B+sin⁡2Ccos⁡2A+cos⁡2B+cos⁡2C=2 \frac{\sin^2 A + \sin^2 B + \sin^2 C}{\cos^2 A + \cos^2 B + \cos^2 C} = 2 is a rectangular triangle.
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