<=> sin4x - 8cos^{4}x + 8cos^{2}x -2 = 4(sinx +cosx)<=> sin4x - 2( 2cos^{2}x -1)^{2} =4(sinx+cosx)<=> 2sin2xcos2x - 2cos^{2}2x -4(sinx+cosx)<=> 2cos2x(sin2x-cos2x) = 4(sinx+cosx)<=> 2(sinx+cosx)(cosx-sinx)(sin2x-cos2x)=4(sinx+cosx)<=> tanx =1hoac 2(cosx -sinx)(sin2x-cos2x)-4=0 (*)(*)<=> -2\sqrt{2}sin(x+pi/4)\sqrt{2}sin(2x+pi/4)-4=0<=>4sin(x+pi/4)sin(2x+pi/4)+4=0<=> 2cosx -2cos(3x+pi/2)+4=0<=> 2cosx+2sin3x+4=0
<=> sin4x - 8cos^{4}x + 8cos^{2}x -2 = 4(sinx +cosx)<=> sin4x - 2( 2cos^{2}x -1)^{2} =4(sinx+cosx)<=> 2sin2xcos2x - 2cos^{2}2x -4(sinx+cosx)=0<=> 2cos2x(sin2x-cos2x) = 4(sinx+cosx)<=> 2(sinx+cosx)(cosx-sinx)(sin2x-cos2x)=4(sinx+cosx)<=> tanx =1hoac 2(cosx -sinx)(sin2x-cos2x)-4=0 (*)(*)<=> -\sqrt{2}cos(x-pi/4)\sqrt{2}sin(2x+pi/4)-2=0<=>2cos(x-pi/4)sin(2x+pi/4)+2=0<=> sin3x+sin(x+pi/2)=-2<=> sin3x+cosx=-2xay ra khi cosx =-1 sỉn3x =-1vo li loai