Cosx+cos3x=cos2x

Question

Cosx+cos3x=cos2x

Answer 1

Cosx+cos3x=cos2x 2cos((x+3x)/2)*cos((x-3x)/2)=cos2x 2cos2xcosx-cos2x=0 cos2x (2cosx-1)=0 cos2x=0 ili 2cosx-1=0 2x=pi/2 + пn cosx=0.5 x = п/4 + пn/2, x= ±п/3 +2пn, n∈Z