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In triangleABC, prove that cos^(2)A+cos^...

In `triangleABC`, prove that `cos^(2)A+cos^(2)B+cos^(2)Cge(3)/(4)`.

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To prove that \( \cos^2 A + \cos^2 B + \cos^2 C \geq \frac{3}{4} \) in triangle \( ABC \), we can follow these steps: ### Step 1: Use the identity for angles in a triangle In any triangle, the sum of angles is \( A + B + C = 180^\circ \). We can use this identity to express one of the angles in terms of the others. ### Step 2: Express \( \cos^2 C \) Using the identity \( C = 180^\circ - (A + B) \), we can write: \[ ...
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