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