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