Cos x-cos 3x=cos 2x-cos4x

помогите решить

-2sin (-x) sin2x=-2sin (-x) sin3x

2sinxsin3x-2sinxsin2x) = 0

2sinx (sin3x-sin2x) = 0

2sinx*2sinx/2*cos5x/2=0

sinx=0⇒x=πn, n∈z

sinx/2=0⇒x/2=πk⇒x=2πk, k∈z

cos5x/2=0⇒5x/2=π/2+πt⇒x=π/5+2πt/5, t∈z