Find the value
Question:

Find the value of $\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)$

Solution:

$\cos ^{-1}\left(\cos \frac{13 \pi}{6}\right)=\cos ^{-1}\left[\cos \left(2 \pi+\frac{\pi}{6}\right)\right]$

$=\cos ^{-1}\left[\cos \left(\frac{\pi}{6}\right)\right]$

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

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