Решите уравнение, с небольшим объяснением, если несложно : ) (1+cosx)/sinx = cos(x/2)

(1+cosx)/sinx)=2cos²(x/2)/(2sin(x/2)cos(x/2))=cos(x/2)/sin(x/2)
cos(x/2)/sin(x/2)=cos(x/2)
cos(x/2)/sin(x/2)-cos(x/2)=0
cos(x/2)-cos(x/2)*sin(x/2)=0, sinx/2≠0
cos(x/2)*(1-sin(x/2))=0
cos(x/2)=0⇒x/2=π/2+πn⇒x=π+2πn,n∈z
sin(x/2)=1⇒x/2=π/2+2πk⇒x=π+4πk,k∈z