Question:
The value of $\sin \left(2\left(\tan ^{-1} 0.75\right)\right)$ is equal to
(a) $0.75$
(b) $1.5$
(c) $0.96$
(d) $\sin ^{-1} 1.5$
Solution:
$\sin \left(2\left(\tan ^{-1} 0.75\right)\right)=\sin \left(2 \tan ^{-1} 0.75\right)$
$=\sin \left(\sin ^{-1} \frac{2 \times 0.75}{1+(0.75)^{2}}\right)$
$=\sin \left(\sin ^{-1} 0.96\right)$
$=0.96$
Hence, the correct answer is option (c).
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