The correct option is B −1
0≤√x2+x+1≤1 and 0≤√x2+x≤1∴ x = −1, 0
For x = −1,L.H.S. = 2 sin−1 1 + cos−1 0 = 2×π2 + π2 = 3π2.∴ x = −1 is a solution.
For x = 0,L.H.S. = 2 sin−1 1 + cos−1 0 = 3π2.Therefore, x = 0 is also a solution.Thus, the sum of solutions = 0 + (−1)= −1.