Question

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

• A. $1$
• B. $-1$
• C. $0$
• D. $\frac{1}{2}$

Answer 1

Answer: (B)

$-1$

For ${\cos }^{-1}xx\in [0,\pi ]$
Hence
$\cos \left\{{\cos }^{-1}(-\frac{\sqrt{3}}{2})+\frac{\pi }{6}\right\}=\cos \{\frac{5\pi }{6}+\frac{\pi }{6}\}=\cos \pi =-1$