y=cosx+sin(π/6-x),x属于【0,π】的最小值和最大值

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y=cosx+sin(π/6-x),x属于【0,π】的最小值和最大值
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y=cosx+sin(π/6-x),x属于【0,π】的最小值和最大值
y=cosx+sin(π/6-x),x属于【0,π】的最小值和最大值

y=cosx+sin(π/6-x),x属于【0,π】的最小值和最大值
y=cosx+sin(π/6)cosx-cos(π/6)sinx
=(3/2)cosx-(√3/2)sinx
=-√3*[sinx*(1/2)-cosx*(√3/2)]
=-√3 [sinx*cos(π/3)-cosx*sin(π/3)]
=-√3sin(x-π/3)
∵ x∈[0,π]
∴ x-π/3∈[-π/3,2π/3]
∴ x-π/3=-π/3,即x=0时,y有最大值3/2
x-π/3=π/2,即x=5π/6时,y有最小值-√3