Question

find the principle value of

$cos - {}^{1} \: \: \: \: \frac{\sqrt{3} }{2}$
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Answer 1

$\huge{\underline{\red{Given:-}}}$

${ \cos }^{ - 1} \: - \sqrt{ \frac {3}{2} } \\ \pi - { \cos }^{ - 1} ( - \sqrt{ \frac{3}{2} } ) \\ \\ let \: { \cos}^{ - 1} ( - \sqrt{ \frac{3}{2} } ) = tita \\ \\ = ( \sqrt{ \frac{3}{2} } ) = \cos \: tita \\ \\ \cos \frac{\pi}{6} = \cos \: tita \\ \\ tita = \frac{\pi}{6} \\ \\ now \\ \\ \pi - { \cos }^{ - 1} ( \sqrt{ \frac{3}{2} } \\ \pi - \frac{\pi}{6} \\ = \frac{5\pi}{6}$

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