Question

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

• A. $\sin {1.2}^{\circ }$
• B. $\sin {1.6}^{\circ }$
• C. $0.48$
• D. $0.96$

Answer 1

The correct option is D $0.96$

$sin\left(2si{n}^{-1}\right(0.8\left)\right)$
$=sin\left(2si{n}^{-1}\right(\frac{4}{5}\left)\right)$
$=2sin\left(si{n}^{-1}\frac{4}{5}\right)cos\left(si{n}^{-1}\frac{4}{5}\right)$
$=2sin\left(si{n}^{-1}\frac{4}{5}\right)cos\left(co{s}^{-1}\frac{3}{5}\right)$
$=2\left(\frac{4}{5}\right)\left(\frac{3}{5}\right)$
$=\frac{24}{25}$
$=0.96$