557 Упростить выражение (cos β/sin α + sin β/cos α) · (1- cos 4α)/cos (π-β + α).

$$\left(\frac{cos \beta}{sin \alpha} + \frac{sin \beta}{cos \alpha}\right) \cdot \frac{1 - cos 4\alpha}{cos(\pi - \beta + \alpha)} = \frac{cos \beta cos \alpha + sin \beta sin \alpha}{sin \alpha cos \alpha} \cdot \frac{1 - cos 4\alpha}{-cos(\alpha - \beta)} = \frac{cos(\alpha - \beta)}{sin \alpha cos \alpha} \cdot \frac{2sin^2 2\alpha}{-cos(\alpha - \beta)} = \frac{2 sin^2 2\alpha}{-sin \alpha cos \alpha} = \frac{2 (2 sin \alpha cos \alpha)^2}{-\frac{1}{2} sin 2\alpha} = \frac{8 sin^2 \alpha cos^2 \alpha}{-\frac{1}{2} sin 2\alpha} = -16 sin \alpha cos \alpha = -8 sin 2\alpha $$

Ответ: $$-8 sin 2\alpha $$