Prove that `2cosx. Cos 3x- 2cos 5x. Cos 7x- cos 4x + cos12x=0`.

Explanation

To prove the equation \(2 \cos x \cos 3x - 2 \cos 5x \cos 7x - \cos 4x + \cos 12x = 0\), we will use trigonometric identities. Let's break it down step by step.

### Step 1: Rewrite the expression using the cosine product-to-sum identities.

We know that:
\[ 2 \cos A \cos B = \cos(A - B) + \cos(A + B) \]
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