Find the general solutions of the following equations: 3x= - Vidyadip

Question

Find the general solutions of the following equations:
$\tan3\text{x}=\cot\text{x}$

✓

Answer

We have,
$\tan3\text{x}=\cot\text{x}$
$\Rightarrow\tan3\text{x}=\tan\Big(\frac{\pi}{2}-\text{x}\Big)\Big[\because\tan\Big(\frac{\pi}{2}-\text{x}\Big)=\cot\text{x}\Big]$
$\Rightarrow3\text{x}=\text{n}\pi+\frac{\pi}{2}-\text{x},\text{n}\in\text{z}$
$\Rightarrow4\text{x}=\text{n}\pi+\frac{\pi}{2},\text{n}\in\text{z}$
$\Rightarrow\text{x}=\frac{\text{n}\pi}{4}+\frac{\pi}{8},\text{n}\in\text{z}$

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