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

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The equation cos^2 A + cos^2 B + cos^2 C + 2*cosA*cosB*cosC = 1 needs to be proven for angles A, B, and C of a triangle, which sum to 180 degrees. A suggested approach involves using the Cosine rule to express the cosines in terms of the triangle's sides. This method may lead to complex algebraic manipulation but is expected to yield the desired result. The discussion highlights the need for a systematic approach to tackle the proof effectively. Overall, utilizing trigonometric identities and properties of triangles is essential for completing the proof.
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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
 
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Welcome to Physicsforums ER901!

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

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