Find the value of ^ - 1 [ ( 13 6 ) ] - Vidyadip

Question

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

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Answer

${\cos ^{ - 1}}\cos \left( {\frac{{13\pi }}{6}} \right) = \frac{{13\pi }}{6}$, but $\frac{{13\pi }}{6} \notin [0,\;\pi ]$
which is principal branch of $\cos^{-1}$
Therefore, $\cos \left( {\frac{{13\pi }}{6}} \right) = \cos \left( {2\pi + \frac{\pi }{6}} \right)$$ = \frac{\pi }{6}$

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