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) ${\sin }^{-1}1.5$

Answer 1

$$\begin{gathered} \sin \left(2\left({\tan }^{-1}0.75\right)\right)=\sin \left(2{\tan }^{-1}0.75\right) \\ =\sin \left({\sin }^{-1}\frac{2\times 0.75}{1+{\left(0.75\right)}^2}\right) \\ =\sin \left({\sin }^{-1}0.96\right) \\ =0.96 \end{gathered}$$
Hence, the correct answer is option (c).