函数y=sin(x-π/6)cosx（x∈[0,3π/4]）

y=sin(x-π/6)cosx
= [sinxcos(π/6) - cosxsin(π/6)] cosx
= cos(π/6)sinxcosx - sin(π/6)cosxcosx
= (1/2)cos(π/6)sin(2x) - sin(π/6)*[cos(2x) + 1)]/2
= (1/2)cos(π/6)sin2x - (1/2)sin(π/6)cos(2x) - (1/2)sin(π/6)
= (1/2)sin(2x - π/6) - 1/4

x∈[0,3π/4]）
2x - π/6 ∈ [-π/6, 4π/3]
sin(2x - π/6) ∈ [sin(4π/3), sin(π/2)] = [-√3 /2, 1]
y ∈ [-(√3 + 1)/4, 1/4]

其最大值为：1/4
最小值为：-3/4

解：y=sin(x-π/6)cosx
=(sinxcosπ/6-cosxsinπ/6)cosx
=√3/2·sinxcosx-1/2·cos²x
=√3/4·sin2x-1/4(2cos²-1)-1/4
=√3/4·sin2x-1/4cos2x+1/4
=1/2(sin2xcosπ/6-cos2xsinπ/6)-1/4
=1/2sin(2x-π/6)-1/4
当x∈[0,3π/4]，-π/6≤2x-π/6≤4π/3
∴-√3/2≤sin(2x-π/6)≤1
∴最大值：1/2-1/4=1/4
最小值:-√3/4-1/4=-(1+√3)/4