已知tanθ=-2√2,求（2cos²θ/2-sinθ-1)/(√2sin(θ+π/4))的值.

已知tanθ=-2√2,求（2cos²θ/2-sinθ-1)/(√2sin(θ+π/4))的值.

（2cos²θ/2-sinθ-1)/(√2sin(θ+π/4))={[2cos(θ/2)-1]-sinθ}/{√2[1/√2cosθ+1/√2sinθ}=( cosθ- sinθ)/( cosθ+sinθ)
=(1-tanθ)/(tanθ+1)
=(1+2√2)(1-2√2)
=-9/7-28√2