Question

sin(x+π/6)cos(x+π/6)>0,25

Answer 1

sin(x+π/6)*cos(x+π/6)>0,25
1/2*(2sin(x+π/6)*cos(x+π/6))>0,25
1/2*sin(2(x+π/6))>0,25
sin(2x+π/3)>0,5
π/6+2πn<2x+π/3<5π/6+2πn, n∈Z
π/6-π/3+2πn<2x<5π/6-π/3+2πn, n∈Z
-π/6+2πn<2x<π/2+2πn, n∈Z
-π/12+πn<x<π/4+πn, n∈Z
x∈(-π/12+πn; π/4+πn), n∈Z