化简【1+sinθ-cosθ/1+sinθ+cosθ】+cot(θ/2)

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化简【1+sinθ-cosθ/1+sinθ+cosθ】+cot(θ/2)

化简【1+sinθ-cosθ/1+sinθ+cosθ】+cot(θ/2)
化简【1+sinθ-cosθ/1+sinθ+cosθ】+cot(θ/2)

化简【1+sinθ-cosθ/1+sinθ+cosθ】+cot(θ/2)
原式=[(1-cosθ)+sinθ]/[(1+cosθ)+sinθ]+cot(θ/2)
=[2sin²(θ/2)+2sin(θ/2)cos(θ/2)]/[2cos²(θ/2)+2sin(θ/2)cos(θ/2)]+cot(θ/2)
=[2sin(θ/2)*(sin(θ/2)+cos(θ/2))]/[2cos(θ/2)(sin(θ/2)+cos(θ/2))]+cot(θ/2)
=sin(θ/2)/cos(θ/2)+cos(θ/2)/sin(θ/2)
=[sin²(θ/2)+cos²(θ/2)]/[sin(θ/2)cos(θ/2)]
=1/(1/2*sinθ)
=2cscθ