1. Zadatak

$$\begin{aligned} 4\cdot2\cdot\sin x\cos x\cdot\cos2x>1&\iff4\cdot\sin2x\cdot\cos2x>1\\ &\iff2\sin4x>1\iff\sin4x>\frac12. \end{aligned}$$

Posljednja nejednakost vrijedi ako je

$$4x\in\left\langle\frac\pi6+2k\pi,\frac{5\pi}6+2k\pi\right\rangle,\qquad k\in\mathbb Z,$$

odnosno,

$$x\in\left\langle\frac\pi{24}+\frac{k\pi}2,\frac{5\pi}{24}+\frac{k\pi}2\right\rangle,\qquad k\in\mathbb Z.$$