The principal solutions of $\sqrt{3} \sec x+2=0$ are

The principal solutions of $\sqrt{3} \sec x+2=0$ are
  1. $\frac{\pi}{6}, \frac{5 \pi}{6}$
  2. $\frac{5 \pi}{6}, \frac{7 \pi}{6}$
  3. $\frac{\pi}{3}, \frac{2 \pi}{3}$
  4. $\frac{2 \pi}{3}, \frac{4 \pi}{3}$

Solution

$\begin{aligned} & \sqrt{3} \sec x+2=0 \\ & \therefore \sec x=\frac{-2}{\sqrt{3}} \Rightarrow \cos x=\frac{-\sqrt{3}}{2} \\ & \therefore \cos x=\cos \left(\pi-\frac{\pi}{6}\right)=\cos \left(\pi+\frac{\pi}{6}\right) \Rightarrow x=\frac{5 \pi}{6}, \frac{7 \pi}{6} \end{aligned}$

Asked in: MHT CET 2021 (20 Sep Shift 2)

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