(tan a/2+1)/(cot a/2+1)=? 怎么得到的？

来源：百度知道 编辑：UC知道 时间：2024/06/23 22:41:29

tan(a/2)=(1-cosa)/sina=sina/(1+cosa)

cot(a/2)=(1+cosa)/sina=sina/(1-cosa)
第一种方法：
(tan a/2+1)/(cot a/2+1)
=(tan²(a/2)+tan(a/2))/(1+tan(a/2))...........上下都×tan(a/2)
=tan(a/2)
=

第二种方法：
(tan a/2+1)/(cot a/2+1)
=((1-cosa)/sina+1)/((1+cosa)/sina+1)
=(1-cosa+sina)/(1+cosa+sina)
=(2sin²(a/2)+2sin(a/2)cos(a/2))/(2cos²(a/2)+2sin(a/2)cos(a/2))
=sin(a/2)(sin(a/2)+cos(a/2))/(cos(a/2)(sin(a/2)+cos(a/2)))
=sin(a/2)/cos(a/2)
=tan(a/2)

(tan a/2+1)/(cot a/2+1)
=2+2/sina

(tan a/2+1)/(cot a/2+1)=2+tg a/2+ctg a/2
=sin a/2/cos a/2+cos a/2/sin a/2+2
=2*(sin^2 a/2+cos^2 a/2)/(2sin a/2*cosa/2)+2
=2/sina+2