The value of sin(2sin^-14/5) is given by :

The correct answer is Option (2) → $\frac{24}{25}$

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

let $θ=\sin^{-1}\frac{4}{5}$

$\sin θ=\frac{4}{5}$ so $\cos θ=\frac{3}{5}$

$\sin(2θ)=2\sin θ\cos θ$

$⇒2×\frac{4×3}{5×5}=\frac{24}{25}$