Verified answer

cos(2x+π/6)> √2/2

  -π/4+2πn≤2x+π/6≤π/4+2πn

 -π/4-π/6+2πn ≤2x≤ π/4-π/6+2πn 

-π/12+2πn≤ 2x≤ ≤π/12+2πn

 -π/24+πn ≤ x ≤ π/24+πn ,  n∈Z