The principal solutions of cot x = sqrt{3} ar | vedclass

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(A) Given $\cot x = \sqrt{3}$.Since $\cot x = \frac{1}{	an x}$,we have $	an x = \frac{1}{\sqrt{3}}$.The principal values of $x$ for which $	an x =

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$\frac{\pi}{6}, \frac{7 \pi}{6}$

Vedclass · Answer

(A) Given $\cot x = \sqrt{3}$.Since $\cot x = \frac{1}{	an x}$,we have $	an x = \frac{1}{\sqrt{3}}$.The principal values of $x$ for which $	an x = \frac{1}{\sqrt{3}}$ lie in the interval $(0, 2\pi)$.In the first quadrant,$	an x = \frac{1}{\sqrt{3}}$ at $x = \frac{\pi}{6}$.Since $	an x$ is positive in the third quadrant,the other solution is $x = \pi + \frac{\pi}{6} = \frac{7\pi}{6}$.Thus,the principal solutions are $\frac{\pi}{6}$ and $\frac{7\pi}{6}$.

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

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