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