Find the general solutions of the following equations: + =0 - Vidyadip

Question

Find the general solutions of the following equations: $\tan\text{mx}+\cot\text{nx}=0$

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Answer

We have, $\tan\text{mx}+\cot\text{nx}=0$ $\sin\text{mx}\sin\text{nx}+\cos\text{mx}\cos\text{nx}=0$ $\cos\text{(m-n)}\text{x}=0$ $\text{(m-n)}\text{x}=\Big(\frac{2\text{k}+1}{2}\Big)\pi$ $\text{x}=\Big(\frac{2\text{k}+1}{2\text{(m-n)}}\Big)\pi,\text{k}\in\text{z}$

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