22.7. Упростите выражение: 3) $$\frac{\sin^2 a - tg^2 a}{\cos^2 a - ctg^2 a}$$

3) $$\frac{\sin^2 a - tg^2 a}{\cos^2 a - ctg^2 a} = \frac{\sin^2 a - \frac{\sin^2 a}{\cos^2 a}}{\cos^2 a - \frac{\cos^2 a}{\sin^2 a}} = \frac{\sin^2 a (1 - \frac{1}{\cos^2 a})}{\cos^2 a (1 - \frac{1}{\sin^2 a})} = \frac{\sin^2 a (1 - \frac{1}{\cos^2 a})}{\cos^2 a (1 - \frac{1}{\sin^2 a})} = \frac{\sin^2 a}{\cos^2 a} \cdot \frac{\cos^2 a - 1}{\cos^2 a} \cdot \frac{\sin^2 a}{\sin^2 a - 1} = tg^2 a \cdot \frac{-\sin^2 a}{\cos^2 a} \cdot \frac{\sin^2 a}{-\cos^2 a} = \frac{\sin^4 a}{\cos^2 a} = tg^4 a$$