Question

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

Answer 1

Consider the given expression.

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

$\Rightarrow \cos [{\cos }^{-1}\left(\cos \frac{5\pi }{6}\right)+\frac{\pi }{6}]$

$\Rightarrow \cos [\frac{5\pi }{6}+\frac{\pi }{6}]$

$\Rightarrow \cos \left(\pi \right)$

$\Rightarrow -1$

Hence, this is the required result.