` cos 6x=32 cos^6 x -48cos^4 x + 18 cos^2 x -1`

Explanation

To prove that \( \cos 6x = 32 \cos^6 x - 48 \cos^4 x + 18 \cos^2 x - 1 \), we will follow these steps:

### Step 1: Start with the left-hand side
We begin with the left-hand side of the equation:
\[ \cos 6x \]
Using the identity for cosine of a multiple angle, we can express \( \cos 6x \) as:
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