Question

$\sin \left[2{\cos }^{-1}\left(-\frac{3}{5}\right)\right]$ is equal to

• A. $\frac{6}{25}$
• B. $\frac{24}{25}$
• C. $\frac{4}{5}$
• D. $-\frac{24}{25}$

Answer 1

Answer: (D)

Put $=co{s}^{-1}\left(-\frac{3}{5}\right)=\theta$
$\Rightarrow cos\theta =-\frac{3}{5}$
$\therefore$ given expression $=sin\left(2\theta \right)$
$=2sin\theta cos\theta \left[\because sin\theta =\frac{4}{5}\right]$
$=2\cdot \frac{4}{5}\left(-\frac{3}{5}\right)$
$=-\frac{24}{25}$