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Evaluatecos[c...

Question

Evaluate
$cos [{cos}^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{6}]$

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Solution

Given :
$cos [{cos}^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{6}]$
$= cos [π - {cos}^{- 1} (\frac{\sqrt{3}}{2}) + \frac{π}{6}]$
$[∵ {cos}^{- 1} (- x) = π - {cos}^{- 1} (x)]$
$= cos [π - \frac{π}{6} + \frac{π}{6}] [∵ {cos}^{- 1} (\frac{\sqrt{3}}{2}) = \frac{π}{6}]$
$= - 1 [∵ cos (π) = - 1]$

Hence, $cos [{cos}^{- 1} (\frac{- \sqrt{3}}{2}) + \frac{π}{6}] = - 1$

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