Question

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

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

Answer 1

The correct option is A $\frac{2\pi }{3}$

${\cos }^{-1}\left(\cot \frac{\pi }{2}\right)+{\cos }^{-1}\left(\sin \frac{2\pi }{3}\right)={\cos }^{-1}\left(0\right)+{\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

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

$=\frac{\pi }{2}+\frac{\pi }{6}$

$=\frac{4\pi }{6}$

$=\frac{2\pi }{3}$