[tex]\sin(3x) = \sin x \\ \\ \Rightarrow 3x = x+2k\pi\quad sau\quad 3x = \pi-x+2k\pi,~~k\in\mathbb{Z} \\ \\ \Rightarrow x = k\pi\quad sau \quad x = \dfrac{\pi}{4}+\dfrac{k\pi}{2}\\ \\ k=0:~~ x = 0\quad sau\quad \boxed{x = \dfrac{\pi}{4}} \\ k = 1:~~x = \pi \quad sau\quad \boxed{x = \dfrac{3\pi}{4}} \\ \\ \text{Doar cele 2 solutii incadrate apartin domeniului.} \\ \\ \Rightarrow S=\Bigg\{\dfrac{\pi}{4}, \dfrac{3\pi}{4}\Bigg\}[/tex]
