Question

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

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

Answer 1

The correct option is A

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

$sin\left(2si{n}^{-1}\sqrt{\frac{63}{65}}\right)$
Use the result $2si{n}^{-1}x=si{n}^{-1}\left(2x\sqrt{1-x^2}\right)$.
$sin\left(si{n}^{-1}\left(2\sqrt{\frac{63}{65}}\sqrt{1-\frac{63}{65}}\right)\right)=2\sqrt{\frac{63}{65}}\sqrt{\frac{2}{65}}=\frac{2\sqrt{126}}{65}$