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  4. sin 2 cos -1((-3/5)) is equal to

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Q. $\sin \left\{2 \cos ^{-1}\left(\frac{-3}{5}\right)\right\}$ is equal to

Inverse Trigonometric Functions

Solution:

$\sin \left\{2 \cos ^{-1}\left(-\frac{3}{5}\right)\right\}$
$=2 \sin \left\{\cos ^{-1}\left(-\frac{3}{5}\right)\right\} \cos \left\{\cos ^{-1}\left(-\frac{3}{5}\right)\right\}$
$=2 \sin \left\{\pi-\cos ^{-1} \frac{3}{5}\right\} \times\left(-\frac{3}{5}\right)$
$=\frac{-6}{5} \sin \left\{\cos ^{-1} \frac{3}{5}\right\}=\frac{-6}{5} \sin \left(\sin ^{-1} \sqrt{1-\frac{9}{25}}\right)$
$=\frac{-6}{5} \times \frac{4}{5}=\frac{-24}{25}$