Prove that: `1+cos2x+cos4x+cos6x=4cosxcos2xcos3x`

Explanation

To prove that \( 1 + \cos 2x + \cos 4x + \cos 6x = 4 \cos x \cos 2x \cos 3x \), we will start with the left-hand side (LHS) and manipulate it to show that it equals the right-hand side (RHS).

### Step 1: Write down the LHS
We begin with the left-hand side:
\[ \text{LHS} = 1 + \cos 2x + \cos 4x + \cos 6x \]

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