3.334. $\frac{\cos 63^{\circ} \cos 3^{\circ}-\cos 87^{\circ} \cos 27^{\circ}}{\cos 132^{\circ} \cos 72^{\circ}-\cos 42^{\circ} \cos 18^{\circ}}=-\tan 24^{\circ}$.
Solution.

$$
\begin{aligned}
& \frac{\cos 63^{\circ} \cos 3^{\circ}-\cos 87^{\circ} \cos 27^{\circ}}{\cos 132^{\circ} \cos 72^{\circ}-\cos 42^{\circ} \cos 18^{\circ}}= \\
& =\frac{\cos 63^{\circ} \cos \left(90^{\circ}-87^{\circ}\right)-\cos 87^{\circ} \cos \left(90^{\circ}-63^{\circ}\right)}{\cos \left(90^{\circ}+42^{\circ}\right) \cos \left(90^{\circ}-18^{\circ}\right)-\cos 42^{\circ} \cos 18^{\circ}}= \\
& =[\sin x \cos y-\cos x \sin y=\sin (x-y) ; \\
& \cos x \cos y+\sin x \sin y=\cos (x-y)]=
\end{aligned}
$$

$$
=\frac{\sin 87^{\circ} \cos 63^{\circ}-\cos 87^{\circ} \sin 63^{\circ}}{-\sin 42^{\circ} \sin 18^{\circ}-\cos 42^{\circ} \cos 18^{\circ}}=\frac{\sin 24^{\circ}}{-\cos 24^{\circ}}=-\tan 24^{\circ}
$$

The equality is valid.