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Prove that costhetacos""(theta)/(2)-cos3...

Prove that `costhetacos""(theta)/(2)-cos3 thetacos""(9theta)/(2)=sin7thetasin8theta`.

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