The function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) is an increasing function in
1
\(\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\)
2
\(\left(0, \frac{\pi}{2}\right)\)
3
\(\left(-\frac{\pi}{2}, \frac{\pi}{4}\right)\)
4
\(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)