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Question
Find the general solution of the following equation:
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Solution
We have:
\[\Rightarrow \tan2x = \frac{1}{\tan x}\]
\[ \Rightarrow \tan2x = \cot x\]
\[ \Rightarrow \tan2x = \tan \left( \frac{\pi}{2} - x \right)\]
\[ \Rightarrow 2x = n\pi + \left( \frac{\pi}{2} - x \right), n \in Z\]
\[ \Rightarrow 3x = n\pi + \frac{\pi}{2}, n \in Z\]
\[ \Rightarrow x = \frac{n\pi}{3} + \frac{\pi}{6}, n \in Z\]
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