Question

Using the principal values, the value of ${\sin }^{-1}\left\{\sin \frac{5\pi }{6}\right\}+{\tan }^{-1}\left\{\tan \frac{\pi }{6}\right\}$ = ?

• A. $\frac{\pi }{6}$
• B. $\frac{2\pi }{3}$
• C. $\frac{\pi }{3}$
• D. $\frac{5\pi }{6}$

Answer 1

Answer: (C)

${\sin }^{-1}\left\{\sin \frac{5\pi }{6}\right\}+{\tan }^{-1}\left\{\tan \frac{\pi }{6}\right\}$
$={\sin }^{-1}\left\{\sin \left(\pi -\frac{\pi }{6}\right)\right\}+\frac{\pi }{6}$
$={\sin }^{-1}\left\{\sin \frac{\pi }{6}\right\}+\frac{\pi }{6}$
$=\frac{\pi }{6}+\frac{\pi }{6}=\frac{2\pi }{6}=\frac{\pi }{3}$