`a^2(cos^2B-cos^2C)+b^2(cos^2C-cos^2A)+c^2(cos^2A-cos^2B)=0` .

Explanation

To prove the equation \( a^2(\cos^2 B - \cos^2 C) + b^2(\cos^2 C - \cos^2 A) + c^2(\cos^2 A - \cos^2 B) = 0 \), we will follow these steps:

### Step 1: Rewrite the Cosine Squares
We know that \( \cos^2 X = 1 - \sin^2 X \). Therefore, we can rewrite each cosine square in the equation:

\[ \cos^2 B = 1 - \sin^2 B, \quad \cos^2 C = 1 - \sin^2 C, \quad \cos^2 A = 1 - \sin^2 A \]
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