Find the principal and general solutions of the following equations:

Q (1)   \small \tan x = \sqrt{3}

Answers (1)

\tan x = \sqrt{3}
 We know that the value of    \tan \frac{\pi}{3} = \sqrt{3}   and  \tan \frac{4\pi}{3} = \tan\left (\pi + \frac{\pi}{3} \right ) = \tan\frac{\pi}{3} Therefore the principle solution is x = \frac{\pi}{3} and \frac{4\pi}{3}

we also know that the value of tan x repeats after an interval of \pi
So,  by this, we can say that 

    \tan x = \tan \frac{\pi}{3} \Rightarrow x = n\pi + \frac{\pi}{3}         where n \epsilon Z

therefore, the general solution is x = n\pi +\frac{\pi}{3}
    

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