y =sinx+√3cosx+2cos²x+√3sin2x的值域为

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y=sinx+√3cosx+2cos²x+√3sin2x的值域为y=sinx+√3cosx+2cos²x+√3sin2x的值域为y=sinx+√3cosx+2cos²x+

y =sinx+√3cosx+2cos²x+√3sin2x的值域为
y =sinx+√3cosx+2cos²x+√3sin2x的值域为

y =sinx+√3cosx+2cos²x+√3sin2x的值域为
y =sinx+√3cosx+2cos²x+√3sin2x
=2(1/2sinx+√3/2cosx)+(cos2x+√3sin2x)+1
=2sin(x+π/3)-2(-1/2cos2x-√3/2sin2x)+1
=2sin(x+π/3)- 2cos(2x+2π/3)+1
=2sin(x+π/3)- 2[1-2sin²(x+π/3)]+1
=4sin²(x+π/3)+2sin(x+π/3)-1
=4[sin(x+π/3)+1/4]²-5/4
∵sin(x+π/3)∈[-1,1]
∴当sin(x+π/3)=-1/4时,ymin=-5/4
当sin(x+π/3)=1时,ymax=5