The equation ^ - 1 x - ^ - 1 x = ^ - 1 ( 3 2 ) has - Vidyadip

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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