(1+sinθ+cosθ)/(sin θ/2+cosθ/2)

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(1+sinθ+cosθ)/(sinθ/2+cosθ/2)(1+sinθ+cosθ)/(sinθ/2+cosθ/2)(1+sinθ+cosθ)/(sinθ/2+cosθ/2)(1+sinθ+cosθ)

(1+sinθ+cosθ)/(sin θ/2+cosθ/2)
(1+sinθ+cosθ)/(sin θ/2+cosθ/2)

(1+sinθ+cosθ)/(sin θ/2+cosθ/2)
(1+sinθ+cosθ)/[sin(θ/2)+cos(θ/2)]
=[2cos²(θ/2)+2sin(θ/2)cos(θ/2)]/[sin(θ/2)+cos(θ/2)]
=2cos(θ/2)[sin(θ/2)+cos(θ/2)]/[sin(θ/2)+cos(θ/2)]
=2cos(θ/2)