Question

The value of ${\cos }^{-1}\left(\cos \frac{5\pi }{3}\right)+{\sin }^{-1}\left(\sin \frac{5\pi }{3}\right)$ is

• A. $0$
• B. $\frac{\pi }{2}$
• C. $\frac{2\pi }{3}$
• D. $\frac{10\pi }{3}$

Answer 1

The correct option is A $0$

${\cos }^{-1}\left(\cos \frac{5\pi }{3}\right)+{\sin }^{-1}\left(\sin \frac{5\pi }{3}\right)={\cos }^{-1}\left[\cos (2\pi -\frac{\pi }{3})\right]+{\sin }^{-1}\left[\sin (2\pi -\frac{\pi }{3})\right]=\frac{\pi }{3}-\frac{\pi }{3}=0.$