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Inverse Trigonometric Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsInverse Trigonometric Functions1 Mark
MCQ
Find the principal values of: $\tan ^{-1}(\sqrt{3})$
  • 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 $\tan ^{-1}(\sqrt{3})=\theta \Rightarrow \tan \theta=\sqrt{3}=\tan \frac{\pi}{3}$
$\Rightarrow \theta=\frac{\pi}{3} \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$
$\therefore$ Principal value of $\tan ^{-1} \sqrt{3}$ is $\frac{\pi}{3}$.

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