Question

One of the principal solutions of $\sqrt{3}secx=-2$ 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, $\sqrt{3}\sec x=-2$
$\Rightarrow \sec x=-\frac{2}{\sqrt{3}}$
$\Rightarrow \cos x=-\frac{\sqrt{3}}{2}=-\cos \frac{\pi }{6}$
$\Rightarrow x=\pi -\frac{\pi }{6}$
$\Rightarrow x=\frac{5\pi }{6}$