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

Gujarat BoardEnglish MediumSTD 12 ScienceMaths2. inverse trigonometric function1 Mark
MCQ
The equation ${\sin ^{ - 1}}x - {\cos ^{ - 1}}x = {\cos ^{ - 1}}\left( {\frac{{\sqrt 3 }}{2}} \right)$ has
  • A
    No solution
  • ✓
    Unique solution
  • C
    Infinite number of solutions
  • D
    None of these
✓

Answer

Correct option: B.
Unique solution
b
(b) We have ${\sin ^{ - 1}}x - {\cos ^{ - 1}}x = {\cos ^{ - 1}}\frac{{\sqrt 3 }}{2} = \frac{\pi }{6}$

But ${\sin ^{ - 1}}x + {\cos ^{ - 1}}x = \frac{\pi }{2}$

$\therefore$ ${\sin ^{ - 1}}x = \frac{\pi }{3}$ and ${\cos ^{ - 1}}x = \frac{\pi }{6}$

==> $x = \frac{{\sqrt 3 }}{2}$ is the unique solution.

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