1
sinx>cosx
sinx-cosx>0/cosx
tgx-1>0
tgx>1
x∈(π/4+πn;π/2+πn,n∈z)
2
sin(x+π/6)*cos(x+π/6)>0,25
0,5sin(2x+π/3)>0,25
sin(2x+π/3)>0,5
π/6+2πn<2x+π/3<5π/6+2πn<br>-π/6+2πn<2x<π/2+2πn<br>-π/12+πnx∈(-π/12+πn;π/4+πn,n∈z)
3
cos²x+sinxcosx≥1
cos²x+sinxcosx-sin²x-cos²x≥0
sinxcosx-sin²x≥0
sin²x-sinxcosx≤0
tg²x-tgx≤0
tgx(tgx-1)≤0
1){tgx≥0
{tgx≤1
x∈[πn;π/4+πn,n∈z]
2)tgx≤0
{tgx≥1
нет решения
4
sin2x+√3cosx≥-1
2(1/2*sin2x+√3/2*cos2x)≥-1
sin(2x+π/3)≥-1/2
-π/6+2πn≤2x+π/3≤7π/6+2πn
-π/2+2πn≤2x≤5π/6+2πn
-π/4+πn≤x≤5π/12+πn,n∈z
x∈[-π/4+πn;5π/12+πn,n∈z]