Question

sinx+sin3x+cosx+cos3x=0

Answer 1

sin(x)+sin(3x)+cos(x)+cos(3x)=0

[sin(x)+sin(3x)]+[cos(x)+cos(3x)]=0

2sin((3x+x)/2)*cos((3x-x)/2)+2cos((3x+x)/2)*cos(3x-x)/2)=0

2sin(2x)*cos(x)+2cos(2x)*cos(x)=0

2*cos(x)*(sin(2x)+cos(2x))=0

1) cos(x)=0

x=pi/2+pi*n

 

2) sin(2x)+cos(2x)=0

sin(2x)=-cos(2x)

sin(2x)/cos(2x)=-cos(2x)/cos(2x)

tg(2x)=-1

2x=arctg(-1)+pi*n

2x=3*pi/4+pi*n

x=3*pi/8+pi*n/2