Неравенства

$$2x - \frac{\pi}{4} = \frac{\pi}{2} + 2\pi k, k \in Z \Leftrightarrow$$ $$\Leftrightarrow 2x = \frac{\pi}{4} + \frac{\pi}{2}+ 2\pi k, k \in Z \Leftrightarrow$$ $$\Leftrightarrow2x = \frac{3\pi}{4} + 2\pi k, k \in Z \Rightarrow x = \frac{3\pi}{8} + \pi k, k \in Z$$

$$x - \frac{3\pi}{4} = \pi + 2\pi k, k\in Z$$ $$x = \frac{3\pi}{4} + \pi + 2\pi k, k\in Z$$ $$x = \frac{7\pi}{4} + 2\pi k, k\in Z$$

$$\cos^2x = \frac{1}{4} \Leftrightarrow \cos x = \pm\frac{1}{2}$$

$$\cos x = \frac{1}{2} \Rightarrow x = \pm\frac{\pi}{3} + 2\pi k, k \in Z$$ $$\cos x = -\frac{1}{2} \Rightarrow x = \pm\frac{2\pi}{3} + 2\pi k, k \in Z$$

$$\sin^2x = \frac{3}{4} \Leftrightarrow \sin x = \pm\frac{\sqrt{3}}{2}$$

$$\sin x = \frac{\sqrt{3}}{2} \Rightarrow x = \frac{\pi}{3} + 2\pi k, k \in Z \quad \text{или} \quad x = \frac{2\pi}{3} + 2\pi k, k \in Z$$ $$\sin x = -\frac{\sqrt{3}}{2} \Rightarrow x = -\frac{\pi}{3} + 2\pi k, k \in Z \quad \text{или} \quad x = -\frac{2\pi}{3} + 2\pi k, k \in Z$$

$$\cos^2 2x = \frac{3}{4} \Leftrightarrow \cos 2x = \pm\frac{\sqrt{3}}{2}$$

$$\cos 2x = \frac{\sqrt{3}}{2} \Rightarrow 2x = \pm\frac{\pi}{6} + 2\pi k, k \in Z$$ $$\cos 2x = -\frac{\sqrt{3}}{2} \Rightarrow 2x = \pm\frac{5\pi}{6} + 2\pi k, k \in Z$$

$$2x = \frac{\pi}{6} + 2\pi k \Rightarrow x = \frac{\pi}{12} + \pi k, k \in Z$$ $$2x = -\frac{\pi}{6} + 2\pi k \Rightarrow x = -\frac{\pi}{12} + \pi k, k \in Z$$ $$2x = \frac{5\pi}{6} + 2\pi k \Rightarrow x = \frac{5\pi}{12} + \pi k, k \in Z$$ $$2x = -\frac{5\pi}{6} + 2\pi k \Rightarrow x = -\frac{5\pi}{12} + \pi k, k \in Z$$