Question

Inverse trigonometric functions ​

Answer 1

$\sf \purple{let}$

$\implies \cos ^{ - 1} ( - \frac{ 4}{5} ) = x$

$\implies \cos(x ) = \frac{ - 4}{5}$

$\implies \sin(x) = \frac{3}{5} \: \: \sf (pyhagoras \: thm.)$

$\sin( 2\cos ^{ - 1} ( - \frac{ 4}{5} ) )$

$\implies \sin(2x)$

$\implies 2 \sin(x) \cos(x)$

$\implies 2 (\frac{ - 4}{5} )( \frac{3}{5} )$

$\orange{\therefore\frac{ - 24}{25} }$

HOPE IT HELPS!!