Find the value

Question:

Find the value of $2 \sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right)$

Solution:

$2 \sec ^{-1} 2+\sin ^{-1}\left(\frac{1}{2}\right)=2 \sec ^{-1}\left(\sec \frac{\pi}{3}\right)+\sin ^{-1}\left(\sin \frac{\pi}{6}\right)$

$=2 \times \frac{\pi}{3}+\frac{\pi}{6}$

$=\frac{5 \pi}{6}$

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