Упр.1150 ГДЗ Макарычев Миндюк Феоктистов 9 класс (Алгебра)

1. $$\frac{1-\cos^2\alpha}{\cos^2\alpha} = \frac{\sin^2\alpha}{\cos^2\alpha} = \operatorname{tg}^2\alpha$$
2. $$\frac{\sin^2\alpha-1}{\sin^2\alpha} = \frac{-\cos^2\alpha}{\sin^2\alpha} = -\operatorname{ctg}^2\alpha$$
3. $$\frac{1-\sin^2\alpha}{1-\cos^2\alpha} = \frac{\cos^2\alpha}{\sin^2\alpha} = \operatorname{ctg}^2\alpha$$
4. $$\operatorname{ctg}^2\alpha+1 = \frac{\cos^2\alpha}{\sin^2\alpha}+1 = \frac{\cos^2\alpha+\sin^2\alpha}{\sin^2\alpha} = \frac{1}{\sin^2\alpha}$$
5. $$\operatorname{tg}^2\alpha+1 = \frac{\sin^2\alpha}{\cos^2\alpha}+1 = \frac{\sin^2\alpha+\cos^2\alpha}{\cos^2\alpha} = \frac{1}{\cos^2\alpha}$$
6. $$1+\operatorname{tg}^2\alpha+\operatorname{ctg}^2\alpha = \frac{1}{\cos^2\alpha}+\frac{\cos^2\alpha}{\sin^2\alpha} = \frac{\sin^2\alpha+\cos^2\alpha}{\sin^2\alpha\cos^2\alpha} = \frac{1}{\sin^2\alpha\cos^2\alpha}$$

Во всех преобразованиях знаменатели исходных выражений должны быть отличны от нуля.