The function f(x)=tan-1(sinx+cosx) is an increasing function in
0,π2
-π2,π2
π4,π2
-π2,π4
Given fx=tan−1sinx+cosxDifferentiate both sides with respect to xf'x=11+sinx+cosx2cosx−sinx=21+sinx+cosx212cosx−12sinx=21+sinx+cosx2cosπ4cosx−sinπ4sinx=2cosx+π41+sinx+cosx2If f'x>0 then fx is increasing function hence fx is increasing if −π2<x+π4<π2It gives x∈−3π4,π4