4

Part of 1952 Polish MO Finals

Problems(1)

cos 3A + cos 3B + cos 3C = 1

Source: Polish MO Finals 1952 p4

Prove that if the angles

A

B

C

of a triangle satisfy the equation

\cos 3A + \cos 3B + \cos 3C = 1,

then one of these angles equals

120^\circ

geometrytrigonometry