Q. $\sin\left( 2\sin^{- 1}\sqrt{\frac{63}{65}} \right)$ is equal to
A) $\frac{2\sqrt{126}}{65}$
B) $\frac{4\sqrt{65}}{65}$
C) $\frac{8\sqrt{63}}{65}$
D) $\frac{\sqrt{63}}{65}$
Explanation
(a)
$\sin{\left( 2\sin^{- 1}\sqrt{\frac{63}{65}} \right) = \sin\left( \sin^{- 1}{2\sqrt{\frac{63}{65}}\sqrt{1 - \frac{63}{65}}} \right)}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sin{\left( \sin^{- 1}\frac{2\sqrt{126}}{65} \right) = \frac{2\sqrt{126}}{65}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.