Prove that: `sin (n + 1) x sin (n + 2)x + cos (n + 1) x cos (n + 2) x = cos x`

Explanation

To prove the identity \( \sin((n+1)x) \sin((n+2)x) + \cos((n+1)x) \cos((n+2)x) = \cos(x) \), we can use the cosine subtraction formula. Here’s a step-by-step solution:

### Step 1: Recall the Cosine Addition Formula
We know that:
\[ \cos(a - b) = \cos a \cos b + \sin a \sin b \]
This formula will be useful for our proof.
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