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

A

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

B

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

C

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

D

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