化简：2cos²α-1/【2sin(π/4-α)sin²(π/4+α)】

化简：2cos²α-1/【2sin(π/4-α)sin²(π/4+α)】
化简：2cos²α-1/【2sin(π/4-α)sin²(π/4+α)】

化简：2cos²α-1/【2sin(π/4-α)sin²(π/4+α)】

利用诱导公式:sin(π/4+α)=cos(π/4-α)
∴ 2cos²α-1/【2sin(π/4-α)sin²(π/4+α)】
=2cos²α-1/【2sin(π/4-α)cos²(π/4-α)】
=cos2α/[sin(π/4-α)*sin(π/2-2α)]
=cos2α/[sin(π/4-α)*cos(2α)]
=1/sin(π/4-α)