The function \(f(x)=\tan ^{-1}(\sin x+\cos x)\) is an increasing function in

\(\left(\frac{\pi}{4}, \frac{\pi}{2}\right)\)

\(\left(-\frac{\pi}{2}, \frac{\pi}{4}\right)\)

\(\left(0, \frac{\pi}{2}\right)\)

\(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)