Principal and general solutions of question tan x=√{3} .

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Trigonometrical Equations

easy

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

Option A

Option B

Option C

Option D

Solution

$\tan x=\sqrt{3}$

It is known that $\tan \frac{\pi}{3}=\sqrt{3}$ and $\tan \left(\frac{4 \pi}{3}\right)=\tan \left(\pi+\frac{\pi}{3}\right)=\tan \frac{\pi}{3}=\sqrt{3}$

Therefore, the principal solutions are $x=\frac{\pi}{3}$ and $\frac{4 \pi}{3}$

Now, $\tan x=\tan \frac{\pi}{3}$

$\Rightarrow x=n \pi+\frac{\pi}{3},$ where $n \in Z$

Therefore, the general solution is $x=n \pi+\frac{\pi}{3},$ where $n \in Z.$

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