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} $