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)

$\sin \left[3{\sin }^{-1}\left(\frac{1}{5}\right)\right]$
$=\sin \left[{\sin }^{-1}\left\{3\left(\frac{1}{5}\right)-4{\left(\frac{1}{5}\right)}^3\right\}\right]$
$=\frac{3}{5}-\frac{4}{125}=\frac{75-4}{125}=\frac{71}{125}$