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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
If ${\cos ^{ - 1}}\left( {\frac{1}{x}} \right) = \theta $, then $\tan \theta  =$
  • A
    $\frac{1}{{\sqrt {{x^2} - 1} }}$
  • B
    $\sqrt {{x^2} + 1} $
  • C
    $\sqrt {1 - {x^2}} $
  • ✓
    $\sqrt {{x^2} - 1} $
✓

Answer

Correct option: D.
$\sqrt {{x^2} - 1} $
d
(d) Given that ${\cos ^{ - 1}}\left( {\frac{1}{x}} \right) = \theta \,\, \Rightarrow \,\,\cos \theta = \frac{1}{x}$

Now, $\tan \theta = \frac{{\sin \theta }}{{\cos \theta }} = \frac{{\sqrt {1 - {{(1/x)}^2}} }}{{1/x}} = \sqrt {{x^2} - 1} $.

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