3. In $\triangle A B C$, it is known that $\angle A=\alpha, C D 、 B E$ are the altitudes on $A B 、 A C$, respectively, then $\frac{D E}{B C}=$ $\qquad$ .
$\begin{array}{l}\text { 3. } \because \quad \angle B D C=\angle B E C, \\ \therefore \quad B, D, E, C \text { are concyclic, } \\ \angle A D E=\angle A C B, \\ \triangle A E D \sim \triangle A B C, \\ \frac{D E^{2}}{B C^{2}}=\frac{S_{\triangle} A E D}{S_{\triangle} A B C}=\frac{A D \cdot A E}{A \cdot A C}=\cos ^{2} \alpha . \\ \therefore \quad \frac{D E}{B C}=|\cos \alpha| .\end{array}$