Q. $\sin\left\lbrack 3\sin^{- 1}\left( \frac{1}{5} \right) \right\rbrack$ is equal to
A) $\frac{71}{125}$
B) $\frac{74}{125}$
C) $\frac{3}{5}$
D) $\frac{1}{2}$
Explanation
(a)
$\sin{\left\lbrack 3\sin^{- 1}\left( \frac{1}{5} \right) \right\rbrack = \sin\left\lbrack \sin^{- 1}\left\{ 3\left( \frac{1}{5} \right) - 4\left( \frac{1}{5} \right)^{3} \right\} \right\rbrack}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{3}{5} - \frac{4}{125} = \frac{71}{125}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.