=>[tex]\frac{sin2x-sin3x+sin4x}{cos2x-cos3x+cos4x}\geq \frac{\sqrt{3}+1}{2}[/tex]
=>[tex]\frac{2.sin3x.cosx-sin3x}{2.cos3x.cosx-cos3x}\geq sin30+cos30[/tex]
=>[tex]\frac{sin3x.(2.cosx-1)}{cos3x.(2.cosx-1)}\geq \frac{\sqrt{3}+1}{2}[/tex]
=>[tex]tan3x\geq \frac{\sqrt{3}+1}{2}[/tex]