Find the principal value of sec-1( 2 3 ). - Vidyadip

Question

Find the principal value of sec^-1$( {\frac{2}{{\sqrt 3 }}} )$.

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Answer

Let ${\sec ^{ - 1}}\left( {\frac{2}{{\sqrt 3 }}} \right) = \theta$
$\sec \theta = \frac{2}{{\sqrt 3 }}$
$\theta \in [0,\;\pi ] - \left\{ {\frac{\pi }{2}} \right\}$
$\implies\sec \theta = \sec \frac{\pi }{6}$
$ = \frac{\pi }{6}$
Principal value of ${\sec ^{ - 1}}\left( {\frac{2}{{\sqrt 3 }}} \right) = \frac{\pi }{6}$

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