1) 3 tg(pi/4-x)<=корень 3
2)
{sinx>=0
{cosx<=-корень 2/2
3)
{cosx*cosy=1/4
{ctgx*ctgy=-3/4
4) cos2x-cos6x=0

1)tg(π/4-x)≤√3/3π/6+πn≤π/4-x<π/2+πnπ/6-π/4+πn≤-x<π/2-π/4+πn-π/24+πn≤-x<π/4+πn-π/4+πn<x≤π/24+πnx∈(-π/4+πn;π/24+πn]2)2πn≤x≤π+2πn3π/4+2πn≤x≤5π/4+2πnx∈[3π/4+2πn;π+2πn}3)cosxcosy=1/4⇒cos(x-y)+cos(x+y)=1/2ctgxctgy--3/4⇒1/4:sinxsiny=-3/4⇒sinxsiny=-1/3⇒cos(x-y)-cos(x+y)=-2/3прибавим и отнимем2сos(x-y)=-1/6⇒cos(x-y)=-1/12⇒x-y=π-argcos1/122cos(x+y)=7/6⇒cos(x+y)=7/12⇒x+y=arccos7/12прибавим и отнимем2x=π-arccos1/12+arccos7/12⇒x=π/2-1/2arccos1/12+1/2arccos7/162y=π-arccos1/12-arccos7/12⇒x=π/2-1/2arccos1/12-1/2arccos7/164)2sin2xsin4x=0sin2x=0⇒2x=πn⇒x=πn/2sin4x=0⇒4x=πn⇒x=πn/4Ответ x=πn/4