1) (sin² α -1)/(1- cos² α) при α = π/4;

Упростим выражение:

$$\frac{\sin^2(\alpha) - 1}{1 - \cos^2(\alpha)} = \frac{-(\underbrace{1 - \sin^2(\alpha)}_{\cos^2(\alpha)})}{\underbrace{1 - \cos^2(\alpha)}_{\sin^2(\alpha)}} = -\frac{\cos^2(\alpha)}{\sin^2(\alpha)} = -\operatorname{ctg}^2(\alpha)$$

Подставим значение $$ \alpha = \frac{\pi}{4} $$:

$$-\operatorname{ctg}^2\left(\frac{\pi}{4}\right) = -1^2 = -1$$

Ответ: -1