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:2024/07/18 18:32:56
![h/sinαsinβ*根号下(sin∧α+sin∧β-2sinαsinβcosαcosβ-2sin∧αsin∧β)这个.怎么化简啊~](/uploads/image/z/3913461-45-1.jpg?t=h%2Fsin%CE%B1sin%CE%B2%2A%E6%A0%B9%E5%8F%B7%E4%B8%8B%EF%BC%88sin%E2%88%A7%CE%B1%2Bsin%E2%88%A7%CE%B2-2sin%CE%B1sin%CE%B2cos%CE%B1cos%CE%B2-2sin%E2%88%A7%CE%B1sin%E2%88%A7%CE%B2%EF%BC%89%E8%BF%99%E4%B8%AA.%E6%80%8E%E4%B9%88%E5%8C%96%E7%AE%80%E5%95%8A%7E)
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)