`y = sinx + cosx`
`<=> \sqrt2(\sin x.\sqrt2/2 + \cos x .\sqrt2/2)`
`<=> \sqrt2(\sin x.\cos \frac{\pi}{4} + \cos x. sin \frac{\pi}{4} )`
`<=> \sqrt2sin(x + \pi/4) `
Ta có:
`-1 ≤ \sin (x + \pi/4) ≤1`
`⇔ -\sqrt2 ≤ \sqrt2sin(x + \pi/4) ≤\sqrt2`
`\Max_{y}=\sqrt{2}` khi `\sin (x+\frac{\pi}{4})=1 \Leftrightarrow (x+\frac{\pi}{4})=\frac{\pi}{2}+k2\pi`
$Min_{y}=-\sqrt{2}$ khi `\sin (x+\frac{\pi}{4})=-1 \Leftrightarrow (x+\frac{\pi}{4})=-\frac{\pi}{2}+k2\pi`
`(k\in\mathbb Z)`.
