This is LaTeX code:

[latex]
 
\sin 3x \sin 2x = \frac{1}{2}[\cos x - \cos 5x] = \frac{1}{2}\cos x - \frac{1}{2} \cos 5x\\
\cos 3x \cos 2x = \frac{1}{2}[\cos 5x + cos x] = \frac{1}{2}\cos 5x + \frac{1}{2}\cos x\\\\
\sin 3x \sin 2x - \cos 3x \cos 2x = \frac{1}{2}\cos x - \frac{1}{2} \cos 5x - \frac{1}{2}\cos 5x - \frac{1}{2}\cos x = \\
= -\cos 5x
 
[/latex]