Упрости выражения: 1) 1 - sin² α

Конечно, сейчас помогу упростить эти выражения! 1) $1 - \sin^2 \alpha = \cos^2 \alpha$ 2) $(1 - \cos \alpha)(1 + \cos \alpha) = 1 - \cos^2 \alpha = \sin^2 \alpha$ 3) $1 + \sin^2 \alpha + \cos^2 \alpha = 1 + 1 = 2$ 4) $\sin \alpha - \sin \alpha \cos^2 \alpha = \sin \alpha (1 - \cos^2 \alpha) = \sin \alpha \sin^2 \alpha = \sin^3 \alpha$ 5) $\sin^4 \alpha + \cos^4 \alpha + 2 \sin^2 \alpha \cos^2 \alpha = (\sin^2 \alpha + \cos^2 \alpha)^2 = 1^2 = 1$ 6) $\tan^2 \alpha - \sin^2 \alpha \tan^2 \alpha = \tan^2 \alpha (1 - \sin^2 \alpha) = \tan^2 \alpha \cos^2 \alpha = \frac{\sin^2 \alpha}{\cos^2 \alpha} \cos^2 \alpha = \sin^2 \alpha$ 7) $\cos^2 \alpha + \tan^2 \alpha \cos^2 \alpha = \cos^2 \alpha (1 + \tan^2 \alpha) = \cos^2 \alpha \frac{1}{\cos^2 \alpha} = 1$ 8) $\tan^2 \alpha (2 \cos^2 \alpha + \sin^2 \alpha - 1) = \tan^2 \alpha (2 \cos^2 \alpha + \sin^2 \alpha - (\cos^2 \alpha + \sin^2 \alpha)) = \tan^2 \alpha (\cos^2 \alpha) = \frac{\sin^2 \alpha}{\cos^2 \alpha} \cos^2 \alpha = \sin^2 \alpha$ 9) $\frac{1 - \tan^2 \alpha + \tan^4 \alpha}{\cos^2 \alpha} = \frac{1}{\cos^2 \alpha} - \frac{\tan^2 \alpha}{\cos^2 \alpha} + \frac{\tan^4 \alpha}{\cos^2 \alpha} = \frac{1}{\cos^2 \alpha} - \frac{\sin^2 \alpha}{\cos^4 \alpha} + \frac{\sin^4 \alpha}{\cos^6 \alpha}$