EQUAZIONE GONIOMETRICA URGENTISSIMISSIMA GRAZIE

[VETTRAMO]

2sin^3x - 2rad3cos^3x - sinx + rad3cosx=0

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[Matlurker]

[math]2sin^3x - 2\sqrt3 cos^3x - sinx + \sqrt3cosx=0\\sinx(2sin^2x-1)-\sqrt3cosx(2cos^2x-1)=0\\sinx(2-2cos^2x-1)-\sqrt3cosx(2cos^2x-1)=0\\-sinx(2cos^2x-1)-\sqrt3cosx(2cos^2x-1)=0\\(2cos^2x-1)(sinx+\sqrt3cosx)=0\\\begin{cases}2cos^2x-1=0\\sinx+\sqrt3cosx=0\end{cases}\\\begin{cases}cosx=\pm \frac{\sqrt 2}{2}\\tgx=-\sqrt3\end{cases}\\\begin{cases}x= \frac{\pi}{4}+k\pi\\ x=\frac{2\pi}{3}+k\pi\end{cases}\\\forall \ k \in \mathbb{Z}[/math]