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