Question

The value of ${\cos }^{-1}(-\frac{1}{2})+{\sin }^{-1}(-\frac{\sqrt{3}}{2})$ is

• A. $\frac{\pi }{3}$
• B. 0
• C. $\frac{2\pi }{3}$
• D. none of these

Answer 1

Answer: (A)

$\frac{\pi }{3}$

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