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Question Number 134538 by bemath last updated on 05/Mar/21

$$$$ How do you find the interval in which x belongs such that |sinx+cosx|=sinx + cosx?\n

Answered by EDWIN88 last updated on 05/Mar/21

$$\mathrm{let}\sin \mathrm{x}+\cos \mathrm{x}=\mathrm{y}\Rightarrow \mathrm{we}\mathrm{get}\mathrm{equation}\mid \mathrm{y}\mid =\mathrm{y}$$ $$\mathrm{this}\mathrm{equation}\mathrm{satisfied}\mathrm{if}\mathrm{only}\mathrm{if}\mathrm{y}⩾0$$ $$\text{Extra close brace or missing open brace}$$ $$\text{Extra close brace or missing open brace}$$ $$\mathrm{n}\mathrm{o}\mathrm{t}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{a}\mathrm{t}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{e}\mathrm{f}\mathrm{u}\mathrm{n}\mathrm{c}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{b}\mathrm{e}⩾0\mathrm{i}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{r}\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{n}\mathrm{d}$$ $$2^{\mathrm{n}\mathrm{d}}\mathrm{q}\mathrm{u}\mathrm{a}\mathrm{d}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{s}\mathrm{o}0⩽\mathrm{x}+\frac{\pi }{4}⩽\pi ;\mathrm{o}\mathrm{r}$$ $$-\frac{\pi }{4}+2\mathrm{k}\pi ⩽\mathrm{x}⩽\frac{3\pi }{4}+2\mathrm{k}\pi .$$

Commented byEDWIN88 last updated on 05/Mar/21

Commented byEDWIN88 last updated on 05/Mar/21

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