Question

$\sin (2{\sin }^{-1}0.8)=$

• A. $0.96$
• B. $0.48$
• C. $0.64$
• D. None of these

Answer 1

The correct option is A

$0.96$

Explanation for the correct answer:

Simplifying the given expression:

$$\begin{gathered} \sin (2{\sin }^{-1}0.8) \\ =\sin \left(2{\sin }^{-1}\left(\frac{4}{5}\right)\right) \\ =\sin \left({\sin }^{-1}2\left(\frac{4}{5}\right)\sqrt{1-\left(\frac{16}{25}\right)}\right)\left[{\sin }^{-1}\left(x\right)={\sin }^{-1}\left(x\right)\left(\sqrt{1-x^2}\right)\right] \\ =\sin \left({\sin }^{-1}\left(\frac{8}{5}\right)\sqrt{1-\left(\frac{16}{25}\right)}\right)\left[\mathrm{Cancelling}\sin \mathrm{and}{\sin }^{-1}\right] \\ =\left(\frac{8}{5}\right)\left(\sqrt{\frac{25-16}{25}}\right) \\ =\left(\frac{8}{5}\right)\left(\sqrt{\frac{9}{25}}\right) \\ =\left(\frac{8}{5}\right)\left(\frac{3}{5}\right) \\ =\frac{24}{25} \\ =0.96 \end{gathered}$$

Therefore, the correct answer is option (A).