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STD 12 - 2. inverse trigonometric function — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 2. inverse trigonometric function1 Mark
MCQ
${\sin ^{ - 1}}x + {\sin ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}x + {\cos ^{ - 1}}\frac{1}{x} = $
  • ✓
    $\pi $
  • B
    $\frac{\pi }{2}$
  • C
    $\frac{{3\pi }}{2}$
  • D
    None of these
✓

Answer

Correct option: A.
$\pi $
a
(a) ${\sin ^{ - 1}}x + {\sin ^{ - 1}}\frac{1}{x} + {\cos ^{ - 1}}x + {\cos ^{ - 1}}\frac{1}{x}$

$= \{ {\sin ^{ - 1}}(x) + {\cos ^{ - 1}}(x)\} + \left\{ {{{\sin }^{ - 1}}\left( {\frac{1}{x}} \right) + {{\cos }^{ - 1}}\left( {\frac{1}{x}} \right)} \right\}$

$ = \frac{\pi }{2} + \frac{\pi }{2} = \pi $.

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