Cos (x/2-pi/12) (sin (x-pi/3) + 1) = 0

1) cos (x/2-π/12) = 0

x/2-π/12=π/2 + πk, k∈Z

x/2=π/12 + π/2 + πk

x/2 = π/12 + 6π/12 + πk

x/2 = 7π/12 + πk

x = 2 (7π/12 + πk)

x=7π/6 + 2πk, k∈Z

2) sin (x-π/3) + 1=0

sin (x-π/3) = - 1

x-π/3 = - π/2 + 2πn, n∈Z

x=π/3 - π/2 + 2πn

x=2π/6 - 3π/6 + 2πn

x = - π/6 + 2πn, n∈Z

Ответ: 7π/6 + 2πk, k∈Z;

- π/6 + 2πn, n∈Z