Question

A solution of $si{n}^{-1}\left(1\right)-si{n}^{-1}\left(\sqrt{3}/x^2\right)-\pi /6=0$ is

• A. $x=-\sqrt{2}$
• B. $x=1$
• C. $x=\sqrt{2}$
• D. $x=1/\sqrt{2}$

Answer 1

Answer: (A), (C)

$x=-\sqrt{2}$
$x=\sqrt{2}$

Given, ${\sin }^{-1}\left(1\right)-{\sin }^{-1}\left(\sqrt{3}/x^2\right)-\pi /6=0$

Simplifying, we get
$\frac{\pi }{2}-\frac{\pi }{6}={\sin }^{-1}\frac{\sqrt{3}}{x^2}$
$\frac{\pi }{3}={\sin }^{-1}\left(\frac{\sqrt{3}}{x^2}\right)$
$\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{x^2}$
$x^2=2$
$\therefore x=\pm \sqrt{2}$