write the value of sin(2sin^-13/5)

Dear Student,

Please find below the solution to the asked query :
$$\begin{gathered} \sin \left(2{\sin }^{-1}\frac{3}{5}\right) \\ =2\sin \left(si{n}^{-1}\frac{3}{5}\right)\cos \left(si{n}^{-1}\frac{3}{5}\right) \\ = 2\times \frac{3}{5}\times cos\left(si{n}^{-1}\frac{3}{5}\right) \\ Let si{n}^{-1}\frac{3}{5}= x \\ \sin x = \frac{3}{5} \\ \cos x = \sqrt{1-{\left(\frac{3}{5}\right)}^2}=\frac{4}{5} \\ So we get, \\ = 2\times \frac{3}{5}\times cos\left(si{n}^{-1}\frac{3}{5}\right) \\ = \frac{6}{5}\times \frac{4}{5}= \frac{24}{25} \end{gathered}$$


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