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

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

Solution

The given equation is $\cot \theta=\sqrt{3}$ which is same $\tan \theta=\frac{1}{\sqrt{3}}$. We know that, $\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}$ and $\tan (\pi+\theta)=\tan \theta$ $\therefore \tan \frac{\pi}{6}=\tan \left(\pi+\frac{\pi}{6}\right)=\tan \frac{7 \pi}{6}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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