Question

1-cos(пи+x)-sin(3пи+x)/2=0
решить уравнение

Answer 1

1+сosx+cos(x/2)=0
2cos²(x/2)+cos(x/2)=0
cos(x/2)*(2cos(x/2)+1)=0
cos(x/2)=0⇒x/2=π/2+πn⇒x=π+2πn,n∈Z
cos(x/2)=-1/2⇒x/2=+-2π/3+2πk⇒x=+-4π/3+4πk,k∈Z