1. Tardigrade
  2. Question
  3. Mathematics
  4. Number of real value of x satisfying the equation, arctan √x(x+1)+ arcsin √x(x+1)+1=(π/2) is

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Number of real value of $x$ satisfying the equation, $\arctan \sqrt{x(x+1)}+\arcsin \sqrt{x(x+1)+1}=\frac{\pi}{2}$ is

Inverse Trigonometric Functions

Solution:

$x(x+1) \geq 0 \text { and } 0 \leq x^2+x+1 \leq 1 $
$\Rightarrow x \geq 0 \text { or } x \leq-1 \text { and } x(x+1) \leq 0 $
$x \leq 0 \text { or } x \geq-1$
$\text { Hence } x=0 \text { or } x=-1$