Relationship between cosines in a triangle

Geometry Level 2

Let A , B , C A,B,C be the angles of a triangle. Find the minimum value of the following expression: cos ⁡ 2 ( A ) + cos ⁡ 2 ( B ) + cos ⁡ 2 ( C ) + 2 cos ⁡ ( A ) cos ⁡ ( B ) cos ⁡ ( C ) \cos^2(A) + \cos^2(B) + \cos^2(C) + 2\cos(A)\cos(B)\cos(C)


The answer is 1.00.

Ariel Gershon by Ariel Gershon , 26, Canada

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1 solution

Ritabrata Roy
Aug 22, 2018

For given constraints, it's just

cos^2(A)+cos^2(B)+cos^2(C)=1- 2cos(A)cos(B)cos(C)

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