## Zadatak B-3.7.

Riješite jednadžbu

$$
\sin x-\sqrt{3} \cos x=2 \sin (2010 x)
$$


## Rješenje.

Jednadžba $\sin x-\sqrt{3} \cos x=2 \sin (2010 x)$ dijeljenjem $\mathrm{s} 2$ prelazi u

$$
\begin{aligned}
\frac{1}{2} \sin x-\frac{\sqrt{3}}{2} \cos x & =\sin (2010 x) \\
\cos \frac{\pi}{3} \sin x-\sin \frac{\pi}{3} \cos x & =\sin (2010 x) \\
\sin \left(x-\frac{\pi}{3}\right) & =\sin (2010 x)
\end{aligned}
$$

1. slučaj: $\quad x-\frac{\pi}{3}=2010 x+2 k \pi$, tj. $x=\frac{1}{2009}\left(-\frac{\pi}{3}-2 k \pi\right), k \in \mathbb{Z}$.
2. slučaj: $\quad x-\frac{\pi}{3}=\pi-2010 x+2 k \pi$, tj. $x=\frac{1}{2011}\left(\frac{4 \pi}{3}+2 k \pi\right), k \in \mathbb{Z}$.

