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

The correct option is A $\frac{2\sqrt{126}}{65}$

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

$=\sin \left[{\sin }^{-1}\left(2\sqrt{\frac{63}{65}}\sqrt{1-\frac{63}{65}}\right)\right]$ ....... $[2{\sin }^{-1}x={\sin }^{-1}(2x\sqrt{1-x^2}\left)\right]$

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

$=\frac{2\sqrt{126}}{65}$