The principal solution of $\cot x=\sqrt{3}$ are

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

Solution

$\begin{aligned} & \cot x=\sqrt{3} \quad \Rightarrow \quad \tan x=\frac{1}{\sqrt{3}} \\ & \therefore \frac{1}{\sqrt{3}}=\tan \left(\pi+\frac{\pi}{6}\right)=\tan \left(\frac{\pi}{6}\right) \\ & \Rightarrow \frac{1}{\sqrt{3}}=\tan \left(\frac{7 \pi}{6}\right)=\tan \left(\frac{\pi}{6}\right)\end{aligned}$

Asked in: MHT CET 2021 (24 Sep Shift 1)

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