Question

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

• A. True
• B. False

Answer 1

The correct option is A True

Let ${\cos }^{-1}\left(\frac{1}{2}\right)=x$. Then, $\cos x=\frac{1}{2}=\cos \frac{\pi }{3}$

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

Let ${\sin }^{-1}\left(\frac{1}{2}\right)=y$. Then, $\sin y=\frac{1}{2}=\sin \frac{\pi }{6}$

Therefore, ${\sin }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{6}$

Thus, ${\cos }^{-1}\left(\frac{1}{2}\right)+2{\sin }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{3}+\frac{2\pi }{6}=\frac{\pi }{3}+\frac{\pi }{3}=\frac{2\pi }{3}$