Question

The value of ${\cos }^{-1}\left(\cos \frac{14\pi }{3}\right)$ is ..$A$.. Here, $A$ refers to

• A. $\frac{2\pi }{3}$
• B. $\frac{-\pi }{3}$
• C. $\frac{\pi }{6}$
• D. None of these

Answer 1

Answer: (A)

We have, ${\cos }^{-1}\left(\cos \frac{14\pi }{3}\right)$
$={\cos }^{-1}\left[\cos \left(4\pi +\frac{2\pi }{3}\right)\right]\left\{\because \frac{2\pi }{3}\in [0,\pi ]\right\}$
$={\cos }^{-1}\left(\cos \frac{2\pi }{3}\right)$
$=\frac{2\pi }{3}\left\{\because {\cos }^{-1}(\cos x)=x,x\in [0,\pi ]\right\}$