Write the value

Question:

Write the value of $\tan ^{-1}\left\{2 \sin \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right\}$

Solution:

$\tan ^{-1}\left\{2 \sin \left(2 \cos ^{-1} \frac{\sqrt{3}}{2}\right)\right\}$

$=\tan ^{-1}\left\{2 \sin \left[\cos ^{-1} 2\left(\frac{\sqrt{3}}{2}\right)^{2}-1\right]\right\}$

$=\tan ^{-1}\left[\begin{array}{lll}2 & \sin \left(\cos ^{-1}\right. & \left.\frac{1}{2}\right)\end{array}\right)$

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