1) The principal solutions of $\cot x=\sqrt{3}$ are A) $\frac{\pi}{6},\frac{7\pi}{6}$ B) $\frac{\pi}{3},\frac{7\pi}{3}$ C) $\frac{\pi}{4},\frac{5\pi}{4}$ D) $\frac{\pi}{6},\frac{5\pi}{6}$ Answer: Option AExplanation: we have, $\cot x=\sqrt{3}$ $\cot x=\cot\frac{\pi}{6}$ or $ \cot\left(\pi+\frac{\pi}{6}\right)$ $\therefore$ $ x=\frac{\pi}{6} ,\frac{7\pi}{6}$ $\therefore$ principal solution is $\frac{\pi}{6},\frac{7\pi}{6}$
