`sin x+4 cos x=2+2sin x`
`<=>sin x-4 cos x=-2`
`<=>\sqrt{17}(1/\sqrt{17} sin x-4/\sqrt{17} cos x)=-2`
`<=>1/\sqrt{17} sin x-4/\sqrt{17} cos x=-2/\sqrt{17}`
Đặt `cos \alpha=1/\sqrt{17}` ; `sin \alpha= 4/\sqrt{17}`
`=>cos \alpha sin x-sin \alpha cos x=-2/\sqrt{17}`
`<=>sin(x-\alpha)=-2/\sqrt{17}`
`<=>` $\left[\begin{matrix} x-\alpha=arc sin (\dfrac{-2}{\sqrt{17}})+k2\pi\\ x-\alpha=\pi-arc sin (\dfrac{-2}{\sqrt{17}})+k2\pi\end{matrix}\right.$
`<=>` $\left[\begin{matrix} x=\alpha+arc sin (\dfrac{-2}{\sqrt{17}})+k2\pi\\ x=\alpha+\pi-arc sin (\dfrac{-2}{\sqrt{17}})+k2\pi\end{matrix}\right.$ `(k in ZZ)`
Vậy `S={\alpha+arc sin ([-2]/\sqrt{17})+k2\pi,\alpha+\pi-arc sin ([-2]/\sqrt{17})+k2\pi|k in ZZ,cos \alpha=1/\sqrt{17}` ; `sin \alpha= 4/\sqrt{17}}`
