( ^ - 1 5 13 ) = - Vidyadip

MCQ

$\cos {\rm{ }}\left( {{{\sin }^{ - 1}}\frac{5}{{13}}} \right) = $

✓
$\frac{{12}}{{13}}$
B
$ - \frac{{12}}{{13}}$
C
$\frac{5}{{12}}$
D
None of these

✓

Answer

Correct option: A.

$\frac{{12}}{{13}}$

a
(d)let ${\sin ^{ - 1}}\frac{5}{{13}} = x\,\, \Rightarrow \,\,\sin x = \frac{5}{{13}}$

$ \Rightarrow \,\,\cos x = \sqrt {1 - \frac{{25}}{{169}}} = \frac{{12}}{{13}}$

==>$\,\,\cos \,\left( {{{\sin }^{ - 1}}\frac{5}{{13}}} \right) = \cos \,\,\left( {{{\cos }^{ - 1}}\frac{{12}}{{13}}} \right) = \frac{{12}}{{13}}$

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