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Question Number 113846 by deepraj123 last updated on 15/Sep/20

$$\mathrm{Thr}\mathrm{general}\mathrm{solution}\mathrm{of}\mathrm{the}\mathrm{equation}$$$$\tan 3x=\tan 5x\mathrm{is}$$

Answered by MJS_new last updated on 15/Sep/20

$$x=0+n\pi =n\pi ;n\in \mathbb{Z}$$

Answered by 1549442205PVT last updated on 16/Sep/20

$$\tan 3\mathrm{x}=\tan 5\mathrm{x}\iff 3\mathrm{x}=5\mathrm{x}+\mathrm{k}\pi$$$$\iff \mathrm{x}=\mathrm{k}\frac{\pi }{2}(\mathrm{k}\in \mathbb{Z})$$

Commented by MJS_new last updated on 16/Sep/20

$$\mathrm{both}\tan \frac{3k\pi }{2}\mathrm{and}\tan \frac{5\mathrm{k}\pi }{2}\mathrm{are}\mathrm{not}\mathrm{defined}\mathrm{if}$$$$k=2n+1\Rightarrow k=2n\Rightarrow x=n\pi$$

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