2. Zadatak

Zbog logaritama uvjeti na rješenje su: $\cos x\neq 0$ i $\sin x>0$.

Vrijedi:

$$\begin{aligned} \frac12\log_2(\cos^2x)-(\log_2\sin x-\log_2 4)&=2,\\ \log_2\left(\sqrt{\cos^2x}\right)-\log_2\sin x&=0,\\ \log_2\frac{|\cos x|}{\sin x}&=0,\\ |\cos x|&=\sin x. \end{aligned}$$

Rješenja dane jednadžbe su

$$x=\frac{\pi}{4} \qquad\text{i}\qquad x=\frac{3\pi}{4}.$$