作业帮h/sinαsinβ*根号下（sin∧α+sin∧β-2sinαsinβcosαcosβ-2sin∧αsin∧β）这个.怎么化简啊~
来源：学生作业帮助网 编辑：作业帮 时间：2024/11/24 05:08:45
h/sinαsinβ*根号下（sin∧α+sin∧β-2sinαsinβcosαcosβ-2sin∧αsin∧β）这个.怎么化简啊~
h/sinαsinβ*根号下（sin∧α+sin∧β-2sinαsinβcosαcosβ-2sin∧αsin∧β）
这个.怎么化简啊~
h/sinαsinβ*根号下（sin∧α+sin∧β-2sinαsinβcosαcosβ-2sin∧αsin∧β）这个.怎么化简啊~
设α>β>0
h/sinαsinβ*√（sin^α+sin^β-2sinαsinβcosαcosβ-2sin^αsin^β）
=h/sinαsinβ*√（sin^α+sin^β-2sinαsinβcosαcosβ-sin^αsin^β-sin^αsin^β）
=h/sinαsinβ*√（sin^α+sin^β-2sinαsinβcosαcosβ-(1-cos^α)(1-cos^β)-sin^αsin^β）
=h/sinαsinβ*√[sin^α+sin^β-2sinαsinβcosαcosβ-(1-cos^α-cos^β+cos^αcos^β)-sin^αsin^β]
=h/sinαsinβ*√[sin^α+sin^β-2sinαsinβcosαcosβ-1+cos^α+cos^β-cos^αcos^β-sin^αsin^β]
=h/sinαsinβ*√[sin^α+sin^β+cos^α+cos^β-2sinαsinβcosαcosβ-1-cos^αcos^β-sin^αsin^β]
=h/sinαsinβ*√[1+1-2sinαsinβcosαcosβ-1-cos^αcos^β-sin^αsin^β]
=h/sinαsinβ*√[1-2sinαsinβcosαcosβ-cos^αcos^β-sin^αsin^β]
=h/sinαsinβ*√[1-(sin^αsin^β+2sinαsinβcosαcosβ+cos^αcos^β)]
=h/sinαsinβ*√[1-(sinαsinβ+cosαcosβ)^2]
=h/sinαsinβ*√[1-(cosαcosβ+sinαsinβ)^2]
=h/sinαsinβ*√[1-cos^(α-β)]
=h/sinαsinβ*√[sin^(α-β)]
=h/sinαsinβ*sin(α-β)
=h(sinαcosβ-cosαsinβ )/sinαsinβ
=h(sinαcosβ/sinαsinβ-cosαsinβ/sinαsinβ)
=h(cosβ/sinβ-cosα/sinα)
=h(cotβ-cotα)