Question

Write the value of $\sin \left(2{\sin }^{-1}\frac{3}{5}\right)$

Answer 1

First use,

$\sin \left(2{\sin }^{-1}\frac{3}{5}\right)=\sin 2x$ where $x={\sin }^{-1}\frac{3}{5}$

$\sin x=\frac{3}{5}$

$\cos x=\frac{4}{5}$

$\sin 2x=2\sin x\cos x=2\ast \frac{3}{5}\ast \frac{4}{5}=\frac{24}{25}$