设p=2sinθcosθ-sinθ-cosθ(0<=θ<=π)

t^2=(sinθ-cosθ)^2

t^2=1-2sinθcosθ

2sinθcosθ=1-t^2

(sin^θ+cos^θ)^2=(sin^θ-cos^θ)^2+4sin^θcos^θ=t^2+2-2t^2=2-t^2

sin^θ+cos^θ=√（2-t^2)

所以 p=1-t^2-√（2-t^2)

t=sinθ-cosθ
sinθ-cosθ=√2sin(θ-π/4)
所以 -√2≤t≤√2

2sinθcosθ=t^2-1
p=t^2-1-t=(t-1/2)^2-5/4
pmin=-5/4
pmax=(1-1/2)^2-5/4=-1