اتحادهای مثلثاتی زیر را ثابت کنید: الف) $(\sin \theta + \cos \theta)^2 + (\sin \theta - \cos \theta)^2 = 2$ پ) $(\sin \theta + \cos \theta - 1)(\sin \theta + \cos \theta + 1) = 2 \sin \theta \cos \theta$ ث) $\frac{1 + \sin \theta}{\cos \theta} = \frac{\cos \theta}{1 - \sin \theta}$ چ) $1 - \frac{\sin^2 x}{1 + \cos x} = \cos x$ خ) $\frac{\sin^4 \alpha - \cos^4 \alpha}{\cos^2 \alpha} = (\tan \alpha + 1)(\tan \alpha - 1)$ ب) $\cos^4 \theta - \sin^4 \theta = 2\cos^2 \theta - 1$ ت) $\frac{1}{1 + \cos \theta} + \frac{1}{1 - \cos \theta} = \frac{2}{\sin^2 \theta}$ ج) $\frac{1 + \cot x}{1 + \tan x} = \cot x$ ح) $\frac{1 + \sin \alpha}{1 - \sin \alpha} - \frac{1 - \sin \alpha}{1 + \sin \alpha} = \frac{4 \tan \alpha}{\cos \alpha}$ د) $\sin^4 \theta + \cos^4 \theta = 1 - 2\sin^2 \theta \cos^2 \theta$