Тригонометрическое неравенство [latex]cosx+cos2x+cos3x\ \textless \ 0\\cos2x(2cosx+1)\ \textless \ 0[/latex]

[latex]cosx+cos2x+cos3x\ \textless \ 0\\\\cos2x+(cosx+cos3x)\ \textless \ 0\\\\cos2x+2\cdot cos2x\cdot cosx\ \textless \ 0\\\\cos2x(2cosx+1)\ \textless \ 0\\\\(2cos^2x-1)(2cosx+1)\ \textless \ 0\\\\(\sqrt2cosx-1)(\sqrt2cosx+1)(2cosx+1)\ \textless \ 0\\\\---(-\frac{\sqrt{2}}{2})+++(-\frac{1}{2})---(\frac{\sqrt2}{2})+++\\\\ \left [ {{ cosx\ \textless \ -\frac{\sqrt2}{2}} \atop {-\frac{1}{2}\ \textless \ cosx\ \textless \ \frac{\sqrt3}{2}}} \right. \; \;,\\\\ x\in (\frac{3\pi}{4}+2\pi n;\frac{5\pi}{4}+2\pi n)\cup (\frac{3\pi}{4}+2\pi k;\frac{2\pi}{3}+2\pi k)\cup\\\\\cup (-\frac{2\pi}{3}+2\pi k;-\frac{\pi}{4}+2\pi k)[/latex]