根号(1-cosα/1+cosα)+根号(1+cosα/1-cosα),其中α为第四象限角 怎样化简

问题描述:

根号(1-cosα/1+cosα)+根号(1+cosα/1-cosα),其中α为第四象限角 怎样化简

=根号1-cos²a/(1+cosα)²+根号1-cos²a/(1-cosα)²
=(sina /1+cosα ) +(sina /1-cosα )
=2sina/1-cos²a
=2sina/sin²a
=2/sina

根号(1-cosα/1+cosα)+根号(1+cosα/1-cosα),
=根号(1-cosα)^2/(sinα)^2+根号(1+cosα)^2/(sinα)^2
=-(1-cosα)/sinα)-(1+cosα)/(sinα)
=-2/sina