已知cosθ =-(根号2)/3,θ 属于(π/2,π),求2/sin2θ -cosθ/sinθ

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已知cosθ=-(根号2)/3,θ属于(π/2,π),求2/sin2θ-cosθ/sinθ已知cosθ=-(根号2)/3,θ属于(π/2,π),求2/sin2θ-cosθ/sinθ已知cosθ=-(根

已知cosθ =-(根号2)/3,θ 属于(π/2,π),求2/sin2θ -cosθ/sinθ
已知cosθ =-(根号2)/3,θ 属于(π/2,π),求2/sin2θ -cosθ/sinθ

已知cosθ =-(根号2)/3,θ 属于(π/2,π),求2/sin2θ -cosθ/sinθ
∵2/sin2θ -cosθ/sinθ
=1/sinθcosθ-cosθ/sinθ
=(1-cos^2θ)/sinθcosθ
= sin^2θ/sinθcosθ
=sinθ/cosθ
=tanθ
∵cosθ =-√2/3,θ ∈(π/2,π)
∴tanθ=-√14/2
∴2/sin2θ -cosθ/sinθ=-√14/2