Answer 1

\[\cos 12x - \cos 4x\]
\[ = - 2\sin \left( \frac{12x + 4x}{2} \right) \sin \left( \frac{12x - 4x}{2} \right) \left\{ \because \cos A - \cos B = - 2\sin \left( \frac{A + B}{2} \right) \sin \left( \frac{A - B}{2} \right) \right\}\]
\[ = - 2 \sin 8x \sin 4x\]