/{\Leftrightarrow} {\frac{1}{2}} {\cos4x} - {\frac{\sqrt{3}}{2}} .{\sin4x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}//{\Leftrightarrow} {\frac{1}{2}} (1 - 2. {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}//{\Leftrightarrow} - {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = 0//{\Leftrightarrow} -{\sin2x}.( {\sin 2x} - {\sqrt{3}}. {\cos2x} - 2.{\cosx}) = 0//{\Leftrightarrow} -2{\sin2x}.({\sin(2x - {\Pi/6}) - {\cosx}) = 0/ ta dc: /{\sin2x} =0 va {\sin(2x - {\Pi/6}) - {\cosx} =0 \Leftrightarrow} {\sin(2x - {\Pi/6})= {\sin({\Pi/2} -x)}=0/

${\Leftrightarrow} {\frac{1}{2}} {\cos4x} - {\frac{\sqrt{3}}{2}} .{\sin4x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}$${\Leftrightarrow} {\frac{1}{2}} (1 - 2. {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}$${\Leftrightarrow} - {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = 0$${\Leftrightarrow} -{\sin2x}.( {\sin 2x} - {\sqrt{3}}. {\cos2x} - 2.{\cosx}) = 0$${\Leftrightarrow} -2{\sin2x}.({\sin(2x - {\Pi/6}) - {\cosx}) = 0$ ta dc: ${\sin2x} =0 va {\sin(2x - {\Pi/6}) - {\cosx} =0$ $Leftrightarrow} {\sin(2x - {\Pi/6})= {\sin({\Pi/2} -x)}=0$

{\Leftrightarrow} {\frac{1}{2}} {\cos4x} - {\frac{\sqrt{3}}{2}} .{\sin4x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}{\Leftrightarrow} {\frac{1}{2}} (1 - 2. {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}{\Leftrightarrow} - {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = 0{\Leftrightarrow} -{\sin2x}.( {\sin 2x} - {\sqrt{3}}. {\cos2x} - 2.{\cosx}) = 0{\Leftrightarrow} -2{\sin2x}.({\sin(2x - {\Pi/6}) - {\cosx}) = 0 ta dc: {\sin2x} =0 va {\sin(2x - {\Pi/6}) - {\cosx} =0 \Leftrightarrow} {\sin(2x - {\Pi/6})= {\sin({\Pi/2} -x)}=0

/{\Leftrightarrow} {\frac{1}{2}} {\cos4x} - {\frac{\sqrt{3}}{2}} .{\sin4x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}//{\Leftrightarrow} {\frac{1}{2}} (1 - 2. {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = {\frac{1}{2}}//{\Leftrightarrow} - {\sin^{2}2x}) + {\sqrt{3}}. {\sin 2x}.{\cos2x} + 2.{\sin2x}.{\cosx} = 0//{\Leftrightarrow} -{\sin2x}.( {\sin 2x} - {\sqrt{3}}. {\cos2x} - 2.{\cosx}) = 0//{\Leftrightarrow} -2{\sin2x}.({\sin(2x - {\Pi/6}) - {\cosx}) = 0/ ta dc: /{\sin2x} =0 va {\sin(2x - {\Pi/6}) - {\cosx} =0 \Leftrightarrow} {\sin(2x - {\Pi/6})= {\sin({\Pi/2} -x)}=0/

\sin\ \frac{\Pi}{6}\. \cos4x\ - \cos\\frac{\Pi}{6\}.\sin4x\ + \sin3x\ + \sinx\ =\frac{1}{2}\\frac{1}{2}\. \cos4x\ - \frac{\sqrt{3} }\{2}\. \sin4x\ +2\sin2x\.\cosx\ =\frac{1}{2}\(1- 2\sin^{2} 2x )\ + \sqrt{3}\ \sin2x\ .\cos2x\ + 2\sin2x\ . \cosx\ =\frac{1}{2}\-\sin ^{2} 2x\ + \sqrt{3}\\sin2x\ .\cos2x\ + 2\sin2x \. \cosx\ =0\\sin2x\(-\sin2x\ + \sqrt{3}\.\cos2x \+ 2\cosx)\ =\0 \

\sin \frac{\Pi}{6}. \cos4x - \cos\frac{\Pi}{6}.sin4x + \sin3x + \sinx =\frac{1}{2}\frac{1}{2}. \cos4x - \frac{\sqrt{3} }{2}. \sin4x +2\sin2x.\cosx =\frac{1}{2}(1- 2\sin^{2} 2x ) + \sqrt{3} \sin2x .\cos2x + 2\sin2x . \cosx =\frac{1}{2}-\sin ^{2} 2x + \sqrt{3} \sin2x .\cos2x + 2\sin2x . \cosx =0\sin2x (-\sin2x + \sqrt{3}.\cos2x + 2\cosx) =0

\sin\ \frac{\Pi}{6}\. \cos4x\ - \cos\\frac{\Pi}{6\}.\sin4x\ + \sin3x\ + \sinx\ =\frac{1}{2}\\frac{1}{2}\. \cos4x\ - \frac{\sqrt{3} }\{2}\. \sin4x\ +2\sin2x\.\cosx\ =\frac{1}{2}\(1- 2\sin^{2} 2x )\ + \sqrt{3}\ \sin2x\ .\cos2x\ + 2\sin2x\ . \cosx\ =\frac{1}{2}\-\sin ^{2} 2x\ + \sqrt{3}\\sin2x\ .\cos2x\ + 2\sin2x \. \cosx\ =0\\sin2x\(-\sin2x\ + \sqrt{3}\.\cos2x \+ 2\cosx)\ =\0 \