令sinx+cosx=2sin(x+π/4)=t
∵0≤x≤π/2,π/4≤x+π/4≤3π/4,
∴-√2/2≤sin(x+π/4)≤1
即-√2≤t≤2
(sinx+cosx)^2=1+2sinxcosx=t^2
2sinxcosx=t^2-1
F(x)=t+a(t^2-1)=at^2+t-a,-√2≤t≤2
讨论a取最值
当0＜a＜√2/2时-√2＜-1/a＜0,最小值h（a）=-a
当√2/2≤a＜2时-√2≤-1/a＜-1/2,最小值h（a）=a-√2
当a≥2时,-1/2≤-1/a＜0,最小值为h(a)=3a+2