Упр.1147 ГДЗ Макарычев Миндюк Феоктистов 9 класс (Алгебра)

Используем основное тригонометрическое тождество:

$$\sin^2\alpha+\cos^2\alpha=1.$$

1. $$\sin^2\alpha-\cos^2\alpha+1 =\sin^2\alpha+(1-\cos^2\alpha) =\sin^2\alpha+\sin^2\alpha =2\sin^2\alpha.$$
2. $$1+\cos^2\alpha-\sin^2\alpha =(1-\sin^2\alpha)+\cos^2\alpha =2\cos^2\alpha.$$
3. $$1-\sin^2\alpha-\cos^2\alpha=0.$$
4. $$\sin^2\alpha-1+\cos^2\alpha =\sin^2\alpha+\cos^2\alpha-1 =0.$$
5. $$\cos^2\alpha+2\sin^2\alpha-1 =\cos^2\alpha+\sin^2\alpha+\sin^2\alpha-1 =\sin^2\alpha.$$
6. $$2\cos^2\alpha+\sin^2\alpha-1 =2\cos^2\alpha+\sin^2\alpha-(\sin^2\alpha+\cos^2\alpha) =\cos^2\alpha.$$
7. $$1-\sin^2\alpha-2\cos^2\alpha =\cos^2\alpha-2\cos^2\alpha =-\cos^2\alpha.$$