`#huy`
`y=sin^2x+3sin2x+3cos^2x`
`=sin^2x+cos^2x+3sin2x+2cos^2x`
`=1+3sin2x+2cos^x`
`=1+3sin2x+1+cos2x`
`=2+3sin2x+cos2x`
Dấu `"="` xãy ra
`=>y-2=3sin2x+cos2x`
`=>(y-2)^2=(3sin2x+cos2x)^2<=(3^2+1^2)(sin^(2)2x+cos^(2)2x)=10`
`=>-\sqrt{10}<=y-2<=\sqrt{10}=>2-\sqrt{10}<=y<=2+\sqrt{10}`
`<=>(sin2x)/3=(cos2x)/1<=>tan2x=3<=>2x=arctan3+k\pi<=>x=(arctan3)/2+(k\pi)/2`