MathDB

a^2 cos^2 A = b^2 cos^2 B + c^2 cos^2 C + 2bc cos B cos C cos 2A

Source: Polish MO Finals 1957 p2

August 29, 2024

trigonometrygeometry

Problem Statement

Prove that between the sides

a

b

c

and the opposite angles

A

B

C

of a triangle there is a relationship

a^2 \cos^2 A = b^2 \cos^2 B + c^2 \cos^2 C + 2bc \cos B \cos C \cos 2A.