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(A) Given equation: $	an x = \sqrt{3}$.We know that $	an \frac{\pi}{3} = \sqrt{3}$.Since $	an x$ is positive in the first and third quadrants,the p

Vedclass · Accepted Answer

$x = \frac{\pi}{3}, \frac{4\pi}{3}$ and $x = n\pi + \frac{\pi}{3}, n \in \mathbb{Z}$

Vedclass · Answer

(A) Given equation: $	an x = \sqrt{3}$.We know that $	an \frac{\pi}{3} = \sqrt{3}$.Since $	an x$ is positive in the first and third quadrants,the principal solutions are $x = \frac{\pi}{3}$ and $x = \pi + \frac{\pi}{3} = \frac{4\pi}{3}$.For the general solution,we use the property that if $	an x = 	an \alpha$,then $x = n\pi + \alpha$,where $n \in \mathbb{Z}$.Here,$\alpha = \frac{\pi}{3}$.Therefore,the general solution is $x = n\pi + \frac{\pi}{3}$,where $n \in \mathbb{Z}$.

Find the principal and general solutions of the equation $\tan x = \sqrt{3}$.

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