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Question: Answered & Verified by Expert
The principal solutions of $\sqrt{3} \sec x+2=0$ are
MathematicsTrigonometric EquationsMHT CETMHT CET 2021 (20 Sep Shift 2)
Options:
  • A $\frac{\pi}{6}, \frac{5 \pi}{6}$
  • B $\frac{5 \pi}{6}, \frac{7 \pi}{6}$
  • C $\frac{\pi}{3}, \frac{2 \pi}{3}$
  • D $\frac{2 \pi}{3}, \frac{4 \pi}{3}$
Solution:
2767 Upvotes Verified Answer
The correct answer is: $\frac{5 \pi}{6}, \frac{7 \pi}{6}$
$$
\begin{aligned}
& \sqrt{3} \sec x+2=0 \\
& \therefore \sec x=\frac{-2}{\sqrt{3}} \Rightarrow \cos x=\frac{-\sqrt{3}}{2} \\
& \therefore \cos x=\cos \left(\pi-\frac{\pi}{6}\right)=\cos \left(\pi+\frac{\pi}{6}\right) \Rightarrow x=\frac{5 \pi}{6}, \frac{7 \pi}{6}
\end{aligned}
$$

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