Question

Find the value of the expression
$3{\sec }^{-1}\left(2\right)-6{\sin }^{-1}\left(\frac{1}{2}\right).$

• A. $2\pi$
• B. $\frac{5\pi }{6}$
• C. $0$
• D. $1$

Answer 1

The correct option is C $0$

$\mathrm{Since},{\sec }^{-1}\left(2\right)=\frac{\pi }{3}\mathrm{and}{\sin }^{-1}\frac{1}{2}=\frac{\pi }{6}\therefore 3{\sec }^{-1}\left(2\right)-6{\sin }^{-1}\left(\frac{1}{2}\right)=3\times \frac{\pi }{3}-6\times \frac{\pi }{6}=0.$