求证1/sin2θ + 1/tan2θ +1/sinθ =1/tanθ/2

来源：学生作业帮编辑：神马作文网作业帮分类：数学作业时间：2024/11/17 06:10:23

因为 1/sin2θ + 1/tan2θ =1/sin2θ +cos2θ/sin2θ
=(1+cos2θ)/sin2θ=2(cosθ)^2/(2sinθcosθ)
=cosθ/sinθ
所以1/sin2θ + 1/tan2θ +1/sinθ
=cosθ/sinθ+1/sinθ
=(1+cosθ)/sinθ
=[2cos(θ/2)^2]/[2sin(θ/2)cos(θ/2)]
=[cos(θ/2)]/[sin(θ/2)]
=1/tan(θ/2)

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