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

Question

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

Answer 1

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