Prove that:`costhetacostheta/2-cos3thetacos(9theta)/2=sin7theta\ sin8thetadot`

Explanation

To prove the equation \( \cos \theta \cos \frac{\theta}{2} - \cos 3\theta \cos \frac{9\theta}{2} = \sin 7\theta \sin 8\theta \), we will start with the left-hand side (LHS) and manipulate it step by step.

### Step 1: Rewrite the LHS
We have:
\[ \text{LHS} = \cos \theta \cos \frac{\theta}{2} - \cos 3\theta \cos \frac{9\theta}{2} \]

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