A) \[\frac{71}{125}\]
B) \[\frac{74}{125}\]
C) \[\frac{3}{5}\]
D) \[\frac{1}{2}\]
E) \[\frac{-3}{5}\]
Correct Answer: A
Solution :
\[\sin \left[ 3{{\sin }^{-1}}\left( \frac{1}{5} \right) \right]\] \[=\sin \left[ {{\sin }^{-1}}\left\{ 3\left( \frac{1}{5} \right)-4{{\left( \frac{1}{5} \right)}^{3}} \right\} \right]\] \[=\frac{3}{5}-\frac{4}{125}=\frac{75-4}{125}=\frac{71}{125}\]
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