Prove that:`cos6x=32cos^6x-48cos^4x+18cos^2x-1`

Explanation

To prove that \( \cos 6x = 32 \cos^6 x - 48 \cos^4 x + 18 \cos^2 x - 1 \), we will start with the left-hand side (LHS) and manipulate it to match the right-hand side (RHS).

### Step-by-Step Solution:

1. **Start with the LHS**:
\[ \text{LHS} = \cos 6x \]
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