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Question Number 15301 by Tinkutara last updated on 09/Jun/17

$$\mathrm{With}\mathrm{the}\mathrm{help}\mathrm{of}\mathrm{graph},\mathrm{find}\mathrm{the}$$ $$\mathrm{solution}\mathrm{set}\mathrm{of}\mathrm{inequation}\tan x>-\sqrt{3}.$$

Answered by mrW1 last updated on 09/Jun/17

$$\mathrm{x}\in (\mathrm{n}\pi -\frac{\pi }{3},\mathrm{n}\pi +\frac{\pi }{2})\wedge \mathrm{n}\in \mathbb{Z}$$

Commented byTinkutara last updated on 10/Jun/17

$$\mathrm{But}\mathrm{answer}\mathrm{is}[n\pi -\frac{\pi }{3}<x<n\pi +\frac{\pi }{2}]$$ $$\cup \{n\pi +\frac{2\pi }{3}<x<n\pi +\frac{3\pi }{2}\}$$ $$\mathrm{Your}\mathrm{first}\mathrm{set}\mathrm{is}\mathrm{correct}\mathrm{but}\mathrm{how}\mathrm{to}\mathrm{get}$$ $$\mathrm{the}{2}^{\mathrm{nd}}\mathrm{set}\mathrm{in}\mathrm{union}?$$

Commented bymrW1 last updated on 10/Jun/17

$$\mathrm{the}\mathrm{second}\mathrm{set}\mathrm{is}\mathrm{the}\mathrm{same}\mathrm{as}\mathrm{the}\mathrm{first}.$$ $$\{n\pi +\frac{2\pi }{3}<x<n\pi +\frac{3\pi }{2}\}$$ $$\equiv \{(\mathrm{n}+1)\pi -\frac{\pi }{3}<\mathrm{x}<(\mathrm{n}+1)\pi +\frac{\pi }{2}\}$$ $$\equiv \{\mathrm{m}\pi -\frac{\pi }{3}<\mathrm{x}<\mathrm{m}\pi +\frac{\pi }{2}\}$$ $$\mathrm{since}\mathrm{n}\in \mathbb{Z},\mathrm{in}\mathrm{set}1\mathrm{is}\mathrm{set}2\mathrm{included}.$$

Commented byTinkutara last updated on 10/Jun/17

$$\mathrm{Thanks}\mathrm{Sir}!$$

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