The value of sin

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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