Find the general solutions of the following equations: 2x =1 - Vidyadip

Question

Find the general solutions of the following equations:
$\tan2\text{x}\tan\text{x}=1$

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Answer

We have,
$\tan2\text{x}\tan\text{x}=1$
$\Rightarrow\tan2\text{x}=\frac{1}{\tan\text{x}}$
$\Rightarrow\tan2\text{x}=\cot\text{x}$
$\Rightarrow\tan2\text{x}=\tan\Big(\frac{\pi}{2}-\text{x}\Big)$
$\Rightarrow2\text{x}=\text{n}\pi+\frac{\pi}{2}-\text{x},\text{n}\in\text{z}$
$\Rightarrow3\text{x}=\text{n}\pi+\frac{\pi}{2},\text{n}\in\text{z}$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{3}+\frac{\pi}{6},\text{n}\in\text{z}$

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