Question

$\sin \left(2{\sin }^{-1}\sqrt{\frac{63}{65}}\right)$ is equal to

• A. $\frac{2\sqrt{126}}{65}$
• B. $\frac{4\sqrt{65}}{65}$
• C. $\frac{8\sqrt{63}}{65}$
• D. $\frac{\sqrt{63}}{65}$

Answer 1

Answer: (A)

$\sin \left(2{\sin }^{-1}\sqrt{\frac{63}{65}}\right)$
$=\sin \left({\sin }^{-1}2\sqrt{\frac{63}{65}}\sqrt{1-\frac{63}{65}}\right)$
$=\sin \left({\sin }^{-1}\frac{2\sqrt{126}}{65}\right)$
$=\frac{2\sqrt{126}}{65}$