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

The principal solutions of $\cot x+\sqrt{3}=0$ are
  1. $\frac{5 \pi}{6}, \frac{11 \pi}{6}$
  2. $\frac{\pi}{6}, \frac{7 \pi}{6}$
  3. $\frac{\pi}{6}, \frac{5 \pi}{6}$
  4. $\frac{5 \pi}{6}, \frac{7 \pi}{6}$

Solution

$\begin{aligned} & \cot x+\sqrt{3}=0 \\ & \Rightarrow \cot x=-\sqrt{3} \\ & \Rightarrow x=\pi-\frac{\pi}{6} \text { or } 2 \pi-\frac{\pi}{6} \\ & \Rightarrow x=\frac{5 \pi}{6} \text { or } \frac{11 \pi}{6}\end{aligned}$

Asked in: MHT CET 2022 (10 Aug Shift 2)

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