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