Question

Solve ${\cos }^{-1}\left(\frac{1}{2}\right)-2{\sin }^{-1}\left(-\frac{1}{2}\right)$

• A. $\frac{8\pi }{3}$
• B. $-\frac{8\pi }{3}$
• C. $\frac{7\pi }{3}$
• D. $\frac{\pi }{3}$

Answer 1

The correct option is A $\frac{8\pi }{3}$

Given that,

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

$={\cos }^{-1}\cos \frac{\pi }{3}+2{\sin }^{-1}\sin \left(\frac{7\pi }{6}\right)$

$=\frac{\pi +7\pi }{3}$

$=\frac{8\pi }{3}$

Hence, this is the answer.