xsinx+cosx>1. X€(0;pi/2)

sinx+cosx=sinx+sinx(π/2-x)=2sinπ/4cos(x-π/4)=√2cos(x-π/4)
√2cos(x-π/4)>1
cos(x-π/4)>1/√2
-π/4+2πn<x-π/4<π/4+2πn
2πn<x<π/2+2πn,n∈z
n=0  x∈(0;π/2)