Question

The value of the expresion $\tan \left({\cos }^{-1}\frac{1}{2}+{\tan }^{-1}\left(\frac{-1}{\sqrt{3}}\right)\right)$, is equal to

• A. 0
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. 1

Answer 1

Answer: (C)

$\tan \left({\cos }^{-1}\frac{1}{2}+{\tan }^{-1}\left(\frac{-1}{\sqrt{3}}\right)\right)=\tan \left(\frac{\pi }{3}-\frac{\pi }{6}\right)=\tan \left(\frac{\pi }{6}\right)=\frac{1}{\sqrt{3}}$.