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Question
Write the general solutions of tan2 2x = 1.
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Solution
Given:
\[\tan^2 2x = 1\]
\[ \Rightarrow \tan 2x = \tan \frac{\pi}{4}\]
\[ \Rightarrow 2x = n\pi + \frac{\pi}{4}\]
\[ \Rightarrow x = \frac{n\pi}{2} + \frac{\pi}{8}, n \in Z\]
Hence, the general solution of the equation is
\[\frac{n\pi}{2} + \frac{\pi}{8}, n \in Z .\]
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