Question

One of the principal solutions of $\sqrt{3}\,sec\, x = -2$ is equal to

• A. $\frac{2\pi}{3}$
• B. $\frac{\pi}{6}$
• C. $\frac{5\pi}{6}$
• D. $\frac{\pi}{3}$
• E. $\frac{\pi}{4}$

Answer 1

Answer: (C)

Given, $ \sqrt{3} \sec x=-2 $
$ \Rightarrow \sec x=-\frac{2}{\sqrt{3}} $
$ \Rightarrow \cos x=-\frac{\sqrt{3}}{2}=-\cos \frac{\pi}{6} $
$ \Rightarrow x=\pi-\frac{\pi}{6} $
$ \Rightarrow x=\frac{5 \pi}{6}$