Question

$\cos \left({\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)+\frac{\pi }{6}\right)$

Answer 1

You should know trignometric values of functions ${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$

${\cos }^{-1}\left(\frac{\sqrt{3}}{2}\right)$=30

30+30=60.

And $\cos \left(60\right)=\frac{1}{2}$