494. cosx + cos3x=cos 2x.

cosx+cos3x=cos2x

2cos((3x+x)/2)cos((3x-x)/2)=cos2x

2cos2xcosx=cos2x

2cos2xcosx-cos2x=0

cos2x(2cosx-1)=0

cos2x=0 или cosx=1/2

2x=π/2+πn, n∈Z или x=+-π/3+2πk, k∈Z

x=π/4+πn/2, n∈Z или x=+-π/3+2πk, k∈Z

Ответ: x=π/4+πn/2, n∈Z; x=+-π/3+2πk, k∈Z