Evaluate $\cos \left[ {{{\cos }^{ - 1}}\left( {\frac{{ - \sqrt 3 }}{2}} \right) + \frac{\pi }{6}} \right]$.
Evaluate $\cos \left[ {{{\cos }^{ - 1}}\left( {\frac{{ - \sqrt 3 }}{2}} \right) + \frac{\pi }{6}} \right]$.
Official Solution
VVidaara Team
✓ Verified solution
NCERT & Exemplar
We have, $\cos \left[ {{{\cos }^{ - 1}}\left( {\frac{{ - \sqrt 3 }}{2}} \right) + \frac{\pi }{6}} \right] = \cos \left[ {{{\cos }^{ - 1}}\left( {\cos \frac{{5\pi }}{6}} \right) + \frac{\pi }{6}} \right]$
$= \cos \left( {\frac{{5\pi }}{6} + \frac{\pi }{6}} \right)$
$= \cos \left( {\frac{{6\pi }}{6}} \right)$
$= \cos (\pi ) = - 1$
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