Q1 Find the principal and general solutions of the following equations:

\tan x= \sqrt{3}

 

 

Answers (1)

It is given that given 
\tan x= \sqrt{3}
Now, we know  that \tan\frac{\pi}{3}= \sqrt3 and \tan\frac{4\pi}{3}= \tan \left ( \pi+\frac{\pi}{3} \right )=\sqrt3

Therefore,
the principal solutions of the equation are x = \frac{\pi}{3},\frac{4\pi}{3}
Now,
The general solution is \tan x =\tan \frac{\pi}{3}

x =n{\pi} + \frac{\pi}{3}  where n \ \epsilon \ Z and Z denotes sets of integer

Therefore,  the general solution of the equation is x =n{\pi} + \frac{\pi}{3}  where n \ \epsilon \ Z and Z denotes sets of integer

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