化简cos50(1+根号3tan10)

来源：百度知道 编辑：UC知道 时间：2024/09/28 06:44:25
详细的问题说明，有助于回答者给出准确的答案

原式=cos50(1+√3*sin10/cos10)
=cos50*(√3sin10+cos10)/cos10
=cos50*2sin(10+a)/cos10
其中tana=1/√3,所以此处a=30
所以原式=2cos50sin40/cos10
=2sin(90-50)*sin40/sin(90-10)
=2(sin40)^2/sin80
=2(sin40)^2/2sin40cos40
=sin40/cos40
=tan40

cos50(1+√3*tan10)
=cos50(cos10/cos10+√3*sin10/cos10)
=cos50[(cos10+√3*sin10)/cos10]

cos10+√3*sin10
=1/2cos10+√3/2*sin10
=cos60cos10+sin60sin10
=cos(60-10)
=cos50

cos50[(cos10+√3*sin10)/cos10]
=cos50*(cos50/cos10)
=(cos50)^2/cos10
=(1+cos100)/2cos10

cos100=-sin10

(1+cos100)/2cos10
=1-sin10/2cos10
=(sin5)^2-2sin5con5+(con5)^2/2[(cos5)^2-(sin5)^2]
=(sin5-cos5)^2/2[(cos5)^2-(sin5)^2]
=sin5-cos5/2(sin5+cos5)
=1-tan5/2(1+tan5)

1-tan5/1+tan5
=tan45-tan5/1+tan45tan5
=tan(45-5)
=tan40

1-tan5/2(1+tan5)
=tan40/2