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y=(sinx+2根号2)(cosx+2根号2)=sinxcosx+2根号2(sinx+cosx)+8
=1/2sin2x+4sin(x+π/4)+8
=-1/2cos(2x+π/2)+4sin(x+π/4)+8
=-1/2(1-2sin(x+π/4)^2)+4sin(x+π/4)+8
=sin(x+π/4)^2+4sin(x+π/4)+15/2
=[sin(x+π/4)+2]^2+7/2
因为-1<=sin(x+π/4)<=1
所以1<=sin(x+π/4)+2<=3
0<=[sin(x+π/4)+2]^2<=9
则值域为[0+7/2,9+7/2]即[7/2，25/2]
=1/2sin2x+4sin(x+π/4)+8
=-1/2cos(2x+π/2)+4sin(x+π/4)+8
=-1/2(1-2sin(x+π/4)^2)+4sin(x+π/4)+8
=sin(x+π/4)^2+4sin(x+π/4)+15/2
=[sin(x+π/4)+2]^2+7/2
因为-1<=sin(x+π/4)<=1
所以1<=sin(x+π/4)+2<=3
0<=[sin(x+π/4)+2]^2<=9
则值域为[0+7/2,9+7/2]即[7/2，25/2]
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