Proving Triangle Angles Equation: cos^2 A + cos^2 B + cos^2 C + 2*cosA*cosB*cosC

[ER901]

Homework Statement

I need to prove the following equation:
cos^2 A + cos^2 B + cos^2 C + 2*cosA*cosB*cosC = 1
where A,B,C are the angles of a triangle

Homework Equations

A+B+C = 180

The Attempt at a Solution

I substituted the sum of A,B,C into the equation, and now I have something like
... + cos^2(180-A-C)+... so on, but I don't know what to do next.

Thanks

 

[Gib Z]

Welcome to Physicsforums ER901!

How about using the Cosine rule to express the Cosines as functions of the sides? there's some messy algebra but it should work out fine.