A Symmetric Angle Expression

★ 7/10trigonometry Completing the Square Trigonometric Identities Triangle Geometry Symmetry

Problem

In $\triangle ABC$ , the angles satisfy

y = 2 + \cos C\cos(A - B) - \cos^2 C.

1. Does the value of $y$ change if any two of the angles $A, B, C$ are exchanged? Prove your conclusion. 2. Find the maximum value of $y$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Completing the Square, Trigonometric Identities, Triangle Geometry, Symmetry

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