The number of real roots of the equation tan - 1 x x + 1 + sin - 1 x 2 + x + 1 = π 4 is:

Step-by-step solution

We have, tan - 1 x 2 + x + sin - 1 x 2 + x + 1 = π 4 For equation to be defined, for tan - 1 x x + 1 , x 2 + x ≥ 0 ⇒ x 2 + x + 1 ≥ 1     . . . . 1 And, from domain of sin - 1 x 2 + x + 1 , x 2 + x + 1 ≤ 1       . . . . 2 ∴ from 1   &   2 only possibility that the equation is defined is x 2 + x = 0   ⇒ x = 0 ,   - 1 at x = 0 , tan - 1 x x + 1 + sin - 1 x 2 + x + 1 = 0 + π 2 ≠ π 4 and at x = - 1 , tan - 1 x x + 1