[ 3 , ^ - 1 ( 1 5 ) ] = - Vidyadip

MCQ

$\sin {\rm{ }}\left[ {3\,{{\sin }^{ - 1}}\left( {\frac{1}{5}} \right)} \right] = $

✓
$71/125$
B
$74/125$
C
$3/5$
D
$1/2$

✓

Answer

Correct option: A.

$71/125$

$\sin \left[ {3{{\sin }^{ - 1}}\frac{1}{5}} \right]$
$ = \sin \left[ {{{\sin }^{ - 1}}\left\{ {3{\rm{ }}\left( {\frac{1}{5}} \right) - 4{\rm{ }}{{\left( {\frac{1}{5}} \right)}^3}} \right\}} \right]$
$ = \sin \left[ {{{\sin }^{ - 1}}\left\{ {\frac{3}{5} - \frac{4}{{125}}} \right\}} \right]$
$ = \sin \left[ {{{\sin }^{ - 1}}\left( {\frac{{75 - 4}}{{125}}} \right)} \right]$
$ = \sin \left[ {{{\sin }^{ - 1}}\frac{{71}}{{125}}} \right] = \frac{{71}}{{125}}$.

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