Cosx/2*cosx*cos2x*cos4x=1/16 решите подробно.

Cosx/2*cosx*cos2x*cos4x=1/16

умножим и разделим левую часть на sinx/2

(sinx/2 * Cosx/2*cosx*cos2x*cos4x) / (sinx/2) =

=1/2 * (sinxcosx*cos2x*cos4x) / (sinx/2) = 1/4 * (sin2x*cos2x*cos4x) / (sinx/2) =

=1/8 * (sin4x*cos4x) sin (x/2) = 1/16*sin8x / (sinx/2)

1/16*sin8x / (sinx/2) = 1/16

sin8x / (sinx/2) = 1

sin8x=sinx/2, sinx/2 ≠0

sin8x-sinx/2=0

2sin (15x/4) * cos (17x/4) = 0

sin (15x/4) = 0 ⇒15x/4=πk⇒x=4πk/15, k∈z

cos (17x/4) = 0⇒17x/4=π/2+πk⇒x=2π/15+4πk/15, k∈z