f(x)=-√3sin^2x+sinxcosx
f(x)=-√3(1-cos2x)/2+sin2x/2
f(x)=-√3/2+√3/2*cos2x+1/2*sin2x
f(x)=-√3/2+sin60*cos2x+cos60*sin2x
f(x)=-√3/2+sin(60+2x)
f（α/2）=1/4-√3/2
f(α/2)=-√3/2+sin(30+α)=1/4-√3/2
sin(30+α)=1/4
sin(30+α) = sin30cosα+cos30sinα
1/4 = 1/2cosα+√3/2sinα
1/2=cosα+√3sinα
1/2=√(1-sin^2α)+√3sinα
(1/2-√3sinα)^2=1-sin^2α
1/4-2√3sinα+4sin^2α=1
4sin^2α-2√3sinα-3/4=0
4sin^2α-2√3sinα+3-3-3/4=0
(2sinα-√3)^2-15/4=0
(2sinα-√3-√15/2)(2sinα-√3+√15/2)=0
2sinα-√3-√15/2=0
2sinα-√3-√15/2=0
sinα=√3/2+√15/4>1(舍去)
(2sinα-√3+√15/2)=0
sinα=√3/2-√15/4