The sum of the absolute maximum and absolute minimum values of the function $f(x)=\tan ^{-1}(\sin x-\cos x)$ in the interval $[0, \pi]$ is :

Question

$\tan ^{-1}\left(\frac{1}{\sqrt{2}}\right)-\frac{\pi}{4}$

$\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)-\frac{\pi}{4}$

$\frac{-\pi}{12}$

Please login to view the detailed solution steps...