If ^ - 1 x + ^ - 1 y = 2 3 , then ^ - 1 x + ^ - 1 y = - Vidyadip

MCQ

If ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{{2\pi }}{3},$ then ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y = $

A
$\frac{{2\pi }}{3}$
✓
$\frac{\pi }{3}$
C
$\frac{\pi }{6}$
D
$\pi $

✓

Answer

Correct option: B.

$\frac{\pi }{3}$

b
(b) ${\sin ^{ - 1}}x + {\sin ^{ - 1}}y = \frac{{2\pi }}{3}$

$ \Rightarrow \frac{\pi }{2} - {\cos ^{ - 1}}x + \frac{\pi }{2} - {\cos ^{ - 1}}y = \frac{{2\pi }}{3}$

==> ${\cos ^{ - 1}}x + {\cos ^{ - 1}}y = \pi - \frac{{2\pi }}{3} = \frac{\pi }{3}$.

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