Sin3x*cos(x+п/4)+cos3x*sin(x+п/4)=0 решите, !

sin3x*cos(x+п/4)+cos3x*sin(x+п/4)=0
sin(3x+x+п/4)=0
sin(4x+п/4)=0
4х+П/4=Пn, n∈Z
4x=-П/4+Пn, n∈Z
x=-П/16+Пn/4, n∈Z

Sin(x)+sin(3x)+cos(x)+cos(3x)=0[sin(x)+sin(3x)]+[cos(x)+cos(3x)]=02sin((3x+x)/2)*cos((3x-x)/2)+2cos((3x+x)/2)*cos(3x-x)/2)=02sin(2x)*cos(x)+2cos(2x)*cos(x)=02*cos(x)*(sin(2x)+cos(2x))=01) cos(x)=0x=pi/2+pi*n 2) sin(2x)+cos(2x)=0sin(2x)=-cos(2x)sin(2x)/cos(2x)=-cos(2x)/cos(2x)tg(2x)=-12x=arctg(-1)+pi*n2x=3*pi/4+pi*nx=3*pi/8+pi*n/2