Question

$\sin \left({\cos }^{-1}\left(\tan \left(\frac{\pi }{6}\right)\right)\right)$ is equal to

• A. $\sqrt{\frac{2}{3}}$
• B. $\sqrt{\frac{3}{2}}$
• C. 1
• D. $\sqrt{\frac{4}{3}}$

Answer 1

Answer: (A)

$\sin \left({\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)\right)=\sin \left({\sin }^{-1}\sqrt{1-\frac{1}{3}}\right)=\sqrt{\frac{2}{3}}$