Question

$ \sin \left[ 3{{\sin }^{-1}}\left( \frac{1}{5} \right) \right] $ is equal to:

• A. $ \frac{71}{125} $
• B. $ \frac{74}{125} $
• C. $ \frac{3}{5} $
• D. $ \frac{1}{2} $
• E. $ \frac{-3}{5} $

Answer 1

Answer: (A)

$ \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} $