Sin(x)-cos(x)<1<br>Разделим обе части на √(1²+(-1)²)=√2
1/√2 * sin(x) + (-1/√2)*cos(x)<1/√2<br>Так как sin(-π/4)=-1/√2, а cos(-π/4)=1/√2, то
sin(x)*cos(-π/4)+sin(-π/4)*cos(x)<1/√2<br>sin(x-π/4)<1/√2<br>Отсюда x-π/4∈(-5π/4+2πk; π/4+2πk),
x∈(-π+2πk;π/2+2πk), k∈Z
Ответ: E.