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 follow a systematic approach using trigonometric identities.

### Step-by-Step Solution:

1. **Start with the left-hand side (LHS)**:
\[ LHS = 1 + \cos 2x + \cos 4x + \cos 6x \]
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