Решить неравенство | sin x + cos x |<√2/2

sinx+cosx=sinx+sinx(π/2-x)=2sinπ/4cos(x-π/4)=√2cos(x-π/4)√2|cos(x-π/4)\<√2/2|cos(x-π/4)|<1/2-1/2<cos(x-π/4)<1/2π/3+2πn<x-π/4<2π/3+2πn U 4π/3+2πn<x-π/4<5π/3+2πn7π/12+2πn<x<11π/12+2πn U 19π/12+2πn<23π/12+2πn,n∈z