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)

$\frac{\pi }{3}$

Answer 2

{{\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}
$=\frac{\pi }{6}+\frac{\pi }{6}=\frac{2\pi }{6}=\frac{\pi }{3}$