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Integration of Trigonometric Functions

Write the pri...

Question

Write the principal value of :
$[{cos}^{- 1} \frac{\sqrt{3}}{2} + {cos}^{- 1} (- \frac{1}{2})]$

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Solution

${cos}^{- 1} \frac{\sqrt{3}}{2} + {cos}^{- 1} (- \frac{1}{2})$

$= {cos}^{- 1} \frac{\sqrt{3}}{2} + [π - {cos}^{- 1} (\frac{1}{2})]$

$= \frac{π}{6} + π - \frac{π}{3} = \frac{5 π}{6}$

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