Question Number 205218 by hardmath last updated on 13/Mar/24
$$\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{x}\:=\:? \\ $$
Answered by Sutrisno last updated on 13/Mar/24
$$ \\ $$$$\left(\mid\:\mathrm{sinx}\mid\:+\:\mid\:\mathrm{cosx}\:\mid\:\right)^{\mathrm{2}} =\:\mathrm{1}^{\mathrm{2}} \\ $$$${sin}^{\mathrm{2}} {x}+\mathrm{2}\mid{sinx}\mid\mid{cosx}\mid+{cos}^{\mathrm{2}} {x}=\mathrm{1} \\ $$$$\mid{sin}\mathrm{2}{x}\mid+\mathrm{1}=\mathrm{1} \\ $$$$\mid{sin}\mathrm{2}{x}\mid=\mathrm{0} \\ $$$$\mathrm{2}{x}=\mathrm{0}+{k}.\mathrm{2}\pi\rightarrow{x}={k}.\pi \\ $$$$\mathrm{2}{x}=\pi−\mathrm{0}+{k}.\mathrm{2}\pi\rightarrow{x}=\frac{\pi}{\mathrm{2}}+{k}.\pi \\ $$$$ \\ $$