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Maximusjugend

12 сент. 2015 г., 5:47:45 (8 лет назад)

1)1-cos²x-(cosx+1)=0
(1-cosx)(1+cosx)-(cosx+1)=0
(1+cosx)(1-cosx-1)=0
cosx=-1⇒x=π+2πn
cosx=0⇒x=2πn
2)(tgx-1)(sin²x+3)=0⇒tgx-1=0, sin²x+3>0 при любом х
tgx=1⇒x=π/4+πn
3)2cos(4x-π/6)>√3
cos(4x-π/6)>√3/2
-π/6+2πn<4x-π/6<π/6+2πn
-π/6+π/6+2πn<4x<π/6+π/6+2πn
2πn<4x<π/3+2πn
πn/2<x<π/12+πn/2
x∈(πn/2;π/12+πn/2)
4)sin(π/3-2x)cos(π/3-2x)≥-√3/4
1/2sin(2π/3-4x)≥-√3/4
sin(2π/3-4x)≥-√3/2
-π/3+2πn≤2π/3-4x≤4π/3+2πn
-π/3-2π/3+2πn≤-4x≤4π/3-2π/3+2πn
-π+2πn≤-4x≤2π/3+2πn
-π/6+πn/2≤x≤π/4+πn/2
x∈[-π/6+πn/2;π/4+πn/2]