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STD 12 - 2. inverse trigonometric function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 2. inverse trigonometric function4 Marks
MCQ
Find the principal value of $\tan ^{-1}(-1)$
  • A
    $-\frac{\pi}{6}$
  • B
    $\frac{\pi}{4}$
  • C
    $-\frac{\pi}{2}$
  • ✓
    $-\frac{\pi}{4}$
✓

Answer

Correct option: D.
$-\frac{\pi}{4}$
d
Let $\tan ^{-1}(-1)=\mathrm{y}$

Then, $\tan y=-1=-\tan \left(\frac{\pi}{4}\right)=\tan \left(-\frac{\pi}{4}\right)$

We know that the range of the principal value branch of $\tan ^{-1}$ is $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ and $\tan \left(-\frac{\pi}{4}\right)=-1$

Therefore, the principal value of $\tan ^{-1}(-1)$ is $-\frac{\pi}{4}$

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