cosx=cos4x

решить уравнение 

cosx=cos4x

cosx-cos4x=0

-2sin(x+4x)/2*sin(x-4x)/2=0

2sin(5x/2)*sin(3x/2)=0

sin(5x/2)=0   либо sin(3x/2)=0

5x/2=pik                         3x/2=pik

x=2pik/5, k∈Z                  x=2pik/3, k∈Z