A) \[\frac{2\sqrt{126}}{65}\]
B) \[\frac{4\sqrt{65}}{65}\]
C) \[\frac{8\sqrt{63}}{65}\]
D) \[\frac{\sqrt{63}}{65}\]
Correct Answer: A
Solution :
\[\sin \left( 2{{\sin }^{-1}}\sqrt{\frac{63}{65}} \right)=\sin \left( {{\sin }^{-1}}2\sqrt{\frac{63}{65}}\sqrt{1-\frac{63}{65}} \right)\] \[=\sin \left( {{\sin }^{-1}}2\sqrt{\frac{63}{65}}\frac{\sqrt{2}}{\sqrt{65}} \right)\] \[=\sin \left( {{\sin }^{-1}}\frac{2\sqrt{126}}{65} \right)\] \[=\frac{2\sqrt{126}}{65}\]
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