Answer
$\frac{24}{25}$
Work Step by Step
1. Let $cos^{-1}(\frac{4}{5})=t$, we have $cos(t)=\frac{4}{5}$ and $sin(t)=\frac{3}{5}$
2. $sin(2cos^{-1}(\frac{4}{5}))=sin(2t)=2sin(t)cos(t)=2(\frac{3}{5})(\frac{4}{5})=\frac{24}{25}$
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