[latex] sqrt{3} sin frac{x}{4} -cos frac{x}{4}=0[/latex] [latex]3sin ^{2} x-2sinx*cosx-5cos ^{2} x=0[/latex]

[latex] sqrt{3}sin frac{x}{4} -cos frac{x}{4} =0[/latex][latex]2( frac{ sqrt{3} }{2} sin frac{x}{4} - frac{1}{2} cos frac{x}{4})=0 [/latex][latex]frac{ sqrt{3} }{2} sin frac{x}{4} - frac{1}{2} cos frac{x}{4}=0[/latex][latex] frac{ sqrt{3} }{2} =cos frac{ pi }{6}, frac{1}{2} =sin frac{ pi }{6} [/latex][latex]cos frac{ pi }{6}sin frac{x}{4} -sin frac{ pi }{6} cos frac{x}{4} =0[/latex][latex]sin( frac{x}{4} - frac{ pi }{6} )=0[/latex][latex] frac{x}{4} - frac{ pi }{6} = pi k,[/latex] k∈Z[latex] frac{x}{4} = frac{ pi }{6} +pi k,[/latex] k∈Z[latex]x= frac{2 pi }{3}+ frac{ pi }{4} k,[/latex] k∈Z