Cosx+cos5x=cos3x+cos7x тригонометрия

Cosx + Cosy = 2Cos((x+y)/2)Cos((x-y)/2)

Cosx - Cosy = -2Sin((x+y)/2)Sin((x-y)/2)

2Cos3x*Cos2x = 2Cos5x*Cos2x

2Cos2x(Cos5x - Cos3x)=0

-4Cos2x*Sin4x*Sinx = 0

Cos2x =0,⇒ 2x = π/2 + πk,⇒ x= π/4 + πk/2  k∈Z

Sin4x = 0,⇒ 4x = πk, x = πk/4

Sinx = 0,⇒ x = πk

x= πk/4, x = πk, k∈Z