Let $f(x)=\sin x+\cos x+\tan x+\arcsin x+\arccos x+\arctan x$ . If $M$ and $m$ are maximum and minimum values of $f(x)$ then their arithmetic mean is equal to?
My Approach:
$\arcsin x + \arccos x =\frac{\pi}{2}$, so the equation becomes $\sin x + \cos x + \tan x + \frac{\pi}{2} + \arctan x$ . After this I differentiated this equation but did not came to any conclusion . Also I tried to solve the equation to make something relevant but the equation did not simplified . Please help...