1、
f(x)=sinx(sinx+√3cosx)
=sin²x + √3sinxcosx
= (1 - cos2x)/2 + (√3/2)sin2x
=(√3/2)sin2x - (1/2)cos2x + 1/2
=sin(2x - π/6) + 1/2
0≤x≤π/2
0≤2x≤π
-π/6≤2x - π/6≤5π/6
-1/2≤sin(2x - π/6)≤1
0≤sin(2x - π/6) + 1/2≤3/2
∴f(x)最大值、最小值分别为3/2、 0
2、
cos(2α + π/3) = cos[2(α+π/6)] = 2cos²(α+π/6) - 1=1/8
∴f(α)= sin(2α - π/6) + 1/2
=sin [(2α + π/3) - π/2] + 1/2
= - cos(2α + π/3) + 1/2
= 3/8