The interval in which the function $f(x)=\operatorname{Tan}^{-1}(\sin x+\cos x)$ is an increasing function, is

• A

  $\left(0, \frac{\pi}{2}\right)$
• B

  $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
• Correct answer
  C

  $\left(-\frac{3 \pi}{4}, \frac{\pi}{4}\right)$
• D

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

Hence, the correct answer is option: 'C'.