Question

The principle value of ${\cos }^{-1}\left(\cos \frac{2\pi }{3}\right)+{\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)$ is:

• A. $\pi$
• B. $\pi /2$
• C. $\pi /3$
• D. $4\pi /3$

Answer 1

The correct option is A $\pi$

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

${\text{sin}}^{-1}(\sin \frac{2\pi }{3})={\text{sin}}^{-1}(\frac{\sqrt{3}}{2})=\frac{\pi }{3}$

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