Question

The value of $\sin \left(2{\sin }^{-1}0.8\right)$

• A. $\frac{1}{25}$
• B. $\frac{25}{24}$
• C. $\frac{24}{25}$
• D. $none$

Answer 1

Answer: (C)

$\frac{24}{25}$

Now,

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

$=$$\sin \left(2{\sin }^{-1}\frac{4}{5}\right)$

$=\sin ({\sin }^{-1}2.\frac{4}{5}.\sqrt{1-\frac{4^2}{25}})$ [$2{\sin }^{-1}x={\sin }^{-1}(2.x.\sqrt{1-x^2})$]

$=\sin ({\sin }^{-1}\frac{8}{5}.\frac{3}{5})$

$=\sin \left({\sin }^{-1}\frac{24}{25}\right)$

$=\frac{24}{25}$.