Find the principal and general solutions of t | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $\tan x = \sqrt{3}$.

Similar Questions

The value of $\theta$ between $0^\circ$ and $360^\circ$ satisfying the equation $\tan \theta + \frac{1}{\sqrt{3}} = 0$ is equal to:

The equation $\sqrt{3} \sin x + \cos x = 4$ has

If $\sin \theta + \cos \theta = 1$,then the general value of $\theta$ is

If $\sin \theta = \sin \alpha$,then $\sin \frac{\theta}{3}$ is equal to:

The general solution of the equation $2 \tan \theta - \cot \theta = -1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module