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