The real solutions of the equation tan -1 x x + 1 + sin -1 x 2 + x + 1 = π 2 are

Step-by-step solution

tan -1  x x + 1 + sin -1  x 2 + x + 1 = π 2 ⇒           tan -1  x 2 + x + sin -1  x 2 + x + 1 = π 2 This equation holds true, if x 2 + x ≥ 0   and   0 ≤ x 2 + x + 1 ≤ 1 Now, x 2 + x ≥ 0   and   0 ≤ x 2 + x + 1 ≤ 1 ⇒         x 2 + x ≥ 0   and   x 2 + x + 1 ≤ 1 ∵