Ctg2x+ctg4x=0 решить уравнение

[latex]ctg2x + ctg4x = 0[/latex] [latex] \frac{cos(2x)}{sin(2x)} + \frac{cos(4x)}{sin(4x)} = 0[/latex] [latex]\frac{\sin \left(2x\right)\cos \left(4x\right)+\cos \left(2x\right)\sin \left(4x\right)}{\sin \left(2x\right)\sin \left(4x\right)} = 0[/latex] [latex]\sin \left(2x\right)\cos \left(4x\right)+\cos \left(2x\right)\sin \left(4x\right)=0[/latex][latex]\sin \left(4x+2x\right)=0[/latex] [latex]\sin \left(6x\right)=0[/latex] [latex]6x=0+2\pi n[/latex] [latex]6x=2\pi n[/latex] [latex]\frac{6x}{6}=\frac{2\pi n}{6}[/latex] [latex]x=\frac{\pi n}{3}[/latex] [latex]6x=\pi +2\pi n[/latex] [latex]\frac{6x}{6}=\frac{\pi +2\pi n}{6}[/latex] [latex]x=\frac{\pi +2\pi n}{6}[/latex] [latex]x=\frac{\pi n}{3}[/latex] (ответ)