Question

The sum of roots of the equation ${\cos }^{-1}\left(\cos x\right)=\left[x\right]$, where $[.]$ denotes the greatest integer function is

• A. $2\pi +3$
• B. $\pi +3$
• C. $\pi -3$
• D. $2\pi -3$

Answer 1

The correct option is A $2\pi +3$


From the above graph, clearly there are $5$ solutions
$x=0,1,2,3,2\pi -3$
$\therefore$ Sum of roots $=2\pi +3$