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2. inverse trigonometric function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
Write $\cot ^{-1}\left(\frac{1}{\sqrt{x^{2}-1}}\right), x>1$ in the simplest form.
  • ✓
    $\sec ^{-1} x$
  • B
    $cosec ^{-1} x$
  • C
    $tan ^{-1} x$
  • D
    $cot ^{-1} x$
✓

Answer

Correct option: A.
$\sec ^{-1} x$
a
Let $x=\sec \theta,$ then $\sqrt{x^{2}-1}=\sqrt{\sec ^{2} \theta-1}=\tan \theta$

Therefore, $\cot ^{-1} \frac{1}{\sqrt{x^{2}-1}}=\cot ^{-1}(\cot \theta)$$=\theta=\sec ^{-1} x$

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