Q90 / 180 · KCET 2008 · Mathematics
$\sin \left(2 \sin ^{-1} \sqrt{\frac{63}{65}}\right)$ is equal to
- Correct answerA$\frac{2 \sqrt{126}}{65}$
- B$\frac{4 \sqrt{65}}{65}$
- C$\frac{8 \sqrt{63}}{65}$
- D$\frac{\sqrt{63}}{65}$
Solution
$\sin \left(2 \sin ^{-1} \sqrt{\frac{63}{65}}\right)=\sin \left(\sin ^{-1} 2 \sqrt{\frac{63}{65}} \sqrt{1-\frac{63}{65}}\right)$
$$
\begin{aligned}
&=\sin (\sin \\
&=\sin (\sin \\
&=\frac{2 \sqrt{126}}{65}
\end{aligned}
$$
Hence, the correct answer is option: 'A'.