Question

数学：化简sinθ-cosθ/tanθ-1

请写出用到的公式。（过程）谢谢

Answer 1

结果见图片：

Answer 2

分母tan@-1=sin@/cos@-1=(sin@-cos@)/cos@
原式＝(sin@-cos@)/[(sin@-cos@)/cos@]=cos@

公式tanx=sinx/cosx

Answer 3

原式=(sinθ-cosθ)/(sinθ/cosθ-1)
=(sinθ-cosθ)/[(sinθ-cosθ)/cosθ]
==cosθ

Answer 4

sinθ-cosθ/tanθ-1
=（sinθ-cosθ）/(sinθ/cosθ-cosθ/cosθ)
=（sinθ-cosθ）/(sinθ-cosθ)/cosθ
=cosθ

Answer 5

(sinθ-cosθ)/(tanθ-1)
=cosθ(sinθ-cosθ)/(sinθ-cosθ) 分子分母同时乘cosθ tanθ=sinθ/cosθ
=cosθ
也不知道你是不是以下的式子
sinθ-cosθ/tanθ-1
=sinθ-cosθ/(sinθ/cosθ)-1
=sinθ-cos²θ/sinθ-1
=(sin²θ-cos²θ)/sinθ-1
=-cos2θ/sinθ-1