Question

The value of ${\tan }^{-1}\left[2\sin \left(2{\cos }^{-1}\frac{\sqrt{3}}{2}\right)\right]$ is

• A. $\frac{\pi }{3}$
• B. $\frac{2\pi }{3}$
• C. $\frac{-\pi }{3}$
• D. $\frac{\pi }{6}$

Answer 1

Answer: (A)

Given, ${\tan }^{-1}\left[2\sin \left(2{\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)\right]$
$={\tan }^{-1}\left[2\sin \left(2\times \frac{\pi }{6}\right)\right]$
$={\tan }^{-1}\left[2\sin \left(\frac{\pi }{3}\right)\right]$
$={\tan }^{-1}\left[2\times \frac{\sqrt{3}}{2}\right]$
$={\tan }^{-1}\sqrt{3}=\frac{\pi }{3}$