Question

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

Answer 1

$=si{n}^{-1}\frac{3}{5}=\theta$

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

$=sin2\theta =2sin\frac{\theta }{2}cos\frac{\theta }{2}$

$=cos\frac{\theta }{2}=\frac{4}{5}$

$=sin2\theta =2\times \frac{3}{5}\times \frac{4}{5}$

= $\sin \left(2si{n}^{-1}\frac{3}{5}\right)=\frac{24}{25}$