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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 $cosec ^{-1}(-\sqrt{2})$
  • A
    $-\frac{\pi}{6}$
  • B
    $\frac{\pi}{3}$
  • C
    $-\frac{\pi}{2}$
  • ✓
    $-\frac{\pi}{4}$
✓

Answer

Correct option: D.
$-\frac{\pi}{4}$
d
Let $cosec ^{-1}(-\sqrt{2})=y .$ Then, $cosec\; y=-\sqrt{2}=-\cos e c\left(\frac{\pi}{4}\right)=\cos e c\left(-\frac{\pi}{4}\right)$

We know that the range of the principal value branch of cosec $^{-1}$ is $\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]-\{0\}$ and $cosec \left(-\frac{\pi}{4}\right)=-\sqrt{2}$

Therefore, the principal value of $cosec ^{-1}(-\sqrt{2})$ is $-\frac{\pi}{4}$

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