Find the principal values of: ^ -1 (2)

MCQ

Find the principal values of: $\sec ^{-1}(2)$

A
$\frac{\pi}{6}$
✓
$\frac{\pi}{3}$
C
$\frac{2 \pi}{3}$
D
$\frac{5 \pi}{6}$

✓

Answer

Correct option: B.

$\frac{\pi}{3}$

(b) : Let $\sec ^{-1}(2)=\theta \Rightarrow \sec \theta=2=\sec \frac{\pi}{3}$
$\Rightarrow \theta=\frac{\pi}{3} \in[0, \pi]-\left\{\frac{\pi}{2}\right\}$
$\therefore \quad$ Principal value of $\sec ^{-1}(2)$ is $\frac{\pi}{3}$.

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