Question

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

• A. $\frac{1}{5}$
• B. $\frac{1}{3}$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is D $-\frac{1}{2}$

Consider the given function,

Let,

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

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

$=\cos (\frac{\pi }{6}+\frac{\pi }{2})$

$=\cos \frac{4\pi }{6}$

$=\cos \left(\frac{2\pi }{3}\right)$

$=-\frac{1}{2}$