√2*sinx>1
sinx>1/√2
sinx>√2/2
x=pi/4+2pik . k=z
x=3pi/4+2pik . k=z
x=(pi/4+2pik ; 3pi/4+2pik) . k=z
cos(x+pi/4)≤√3/2
x+pi/4=pi/6+2pik . k=z
x=-p/12+2pik . k=z
x+pi/4=11pi/6+2pik .k=z
x=19pi/12+2pik .k=z
x=[-p/12+2pik ;19pi/12+2pik]
tg2x≥ tg pi/3
tg2x≥√3
2x=pi/3+2pik . k=z
x=pi/6+pik . k=z
2x=-2pi/3+2pik . k=z
x=-pi/3+pik . k=z
x=[pi/6+pik;pi/2+pik) . k=z
√2*sinx>1
sinx>1/√2
sinx>√2/2
x=pi/4+2pik . k=z
x=3pi/4+2pik . k=z
x=(pi/4+2pik ; 3pi/4+2pik) . k=z
cos(x+pi/4)≤√3/2
x+pi/4=pi/6+2pik . k=z
x=-p/12+2pik . k=z
x+pi/4=11pi/6+2pik .k=z
x=19pi/12+2pik .k=z
x=[-p/12+2pik ;19pi/12+2pik]
tg2x≥ tg pi/3
tg2x≥√3
2x=pi/3+2pik . k=z
x=pi/6+pik . k=z
2x=-2pi/3+2pik . k=z
x=-pi/3+pik . k=z
x=[pi/6+pik;pi/2+pik) . k=z