Evaluate $\cos \left[ {{{\cos }^{ – 1}}\left( {\frac{{ – \sqrt 3 }}{2}} \right) + \frac{\pi }{6}} \right]$.<br>[NCERT,Exemplar.2.3,Q.2,Page.35]

Evaluate $\cos \left[ {{{\cos }^{ - 1}}\left( {\frac{{ - \sqrt 3 }}{2}} \right) + \frac{\pi }{6}} \right]$.
[NCERT,Exemplar.2.3,Q.2,Page.35]

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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