Question

Тригонометрические неравенства

Cos(п/2-4x)>-1/2

ctg(2x-п/4)>корень3/3

и

Cos(п/3-5x)<=1/2

tg(2x+п/3)>= -корень3/3

Answer 1

cos(π/2-4x)>-1/2;

sin4x>-1/2;

4x∈(-π/6+2πn; 7π/6+2πn). n∈Z.

x∈(-π/24+πn/2;7π/24+πn/2). n∈Z.

 

ctg(2x-π/4)>1/√3;

πn<2x-π/4<π/3+πn. n∈Z.

π/8+πn/2<x<7π/24+πn/2. n∈Z.

x∈(π/8+πn/2; 7π/24+πn/2). n∈Z.

 

tg(2x+π/3)≥-1/√3;

-π/2+πn<2x+π/3≤-π/6+πn. n∈Z.

-5π/12+πn/2<x≤-π/4+πn/2. n∈Z.

x∈(-5π/12+πn/2; -π/3+πn/2]. n∈Z.