Question

The value of
${\sin }^{-1}(\frac{2\sqrt{2}}{3})+{\sin }^{-1}(\frac{1}{3})$ is equal to

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{2}$
• C. $\frac{\pi }{4}$
• D. $\frac{2\pi }{4}$

Answer 1

Answer: (B)

${\sin }^{-1}\left(\frac{2\sqrt{2}}{3}\right)+{\sin }^{-1}\frac{1}{3}$
$={\sin }^{-1}\left(\frac{2\sqrt{2}}{3}\right)+{\cos }^{-1}\sqrt{1-{\left(\frac{1}{3}\right)}^2}$
$={\sin }^{-1}\left(\frac{2\sqrt{2}}{3}\right)+{\cos }^{-1}\left(\frac{2\sqrt{2}}{3}\right)$
$=\frac{\pi }{2}\left[\because {\sin }^{-1}x+{\cos }^{-1}x=\frac{\pi }{2}\right]$