Ответ:

[tex]\displaystyle \left [ {{x=\pi n-\dfrac\pi2} \atop {x=(-1)^n\arcsin\Big(-\dfrac13\Big) +\pi n}} \right.,~n\in\mathbb{Z}\Bigg.\\\\[/tex]

Пошаговое объяснение:

[tex]\displaystyle 3\cdot\sin x\cdot\cos x+\cos x = 0\Big.\\\cos x~(3\sin x+1)=0\Big.\\\\\left [ {{\cos x=0} \atop {\sin x=-\dfrac13}} \right.\Bigg.\\\\\\\left [ {{x=\pi n-\dfrac\pi2} \atop {x=(-1)^n\arcsin\Big(-\dfrac13\Big) +\pi n}} \right.,~n\in\mathbb{Z}\Bigg.\\\\[/tex]