Question

$sqrt{2} sin ( frac{ pi }{4} + frac{x}{2} ) geq 1$

Answer 1

sin(x/2+π/4)≥1/√2
π/4+2πn≤x/2+π/4≤3π/4+2πn
2πn≤x/2≤π/2+2πn
4πn≤x≤π+4πn,n∈z