The value of $\sin \left(2 \cos ^{-1} \cdot\left(-\frac{3}{5}\right)\right)$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \quad 	ext { Let } \cos ^{-1}\left(\frac{-3}{5}ight)=x \ & \quad \Rightarrow \cos x=\frac{-3}{5} \ & 	herefore \quad \sin x=\sqrt{1-\cos ^2 x}=\sqrt{1-\left(\frac{-3}{5}ight)^2}=\frac{4}{5}\end{aligned}$ $\begin{aligned} 	herefore \quad \sin \left(2 \cos ^{-1}\left(\frac{-3}{5}ight)ight) & =\sin 2 x \ & =2 \sin x \cdot \cos x \ & =2 	imes \frac{4}{5} 	imes \frac{-3}{5} \ & =\frac{-24}{25}\end{aligned}$

The value of $\sin \left(2 \cos ^{-1} \cdot\left(-\frac{3}{5}\right)\right)$ is

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