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函数 f﹙x﹚ = sin ²x +√3sinxcosx 在区间[π/4 , π/2 ] 上的最大值是?
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f(x)=(sinx)^2+√3sinxcosx
=(√3/2)sin2x-(1/2)cos2x+1/2
=sin2xcosπ/6-cos2xsinπ/6+1/2
=sin(2x-π/6)+1/2
π/4<=x<=π/2,则π/3<=2x-π/6<=5π/6
当2x-π/6=π/2、即x=π/3时,f(x)取得最大值f(π/3)=1+1/2=3/2
.
=(√3/2)sin2x-(1/2)cos2x+1/2
=sin2xcosπ/6-cos2xsinπ/6+1/2
=sin(2x-π/6)+1/2
π/4<=x<=π/2,则π/3<=2x-π/6<=5π/6
当2x-π/6=π/2、即x=π/3时,f(x)取得最大值f(π/3)=1+1/2=3/2
.
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