已知α为第四象限角,化简:cosα*根号下(1-sinα)/(1+sinα)+sinα根号下(1-cosα)/(1+cosα)

问题描述:

已知α为第四象限角,化简:cosα*根号下(1-sinα)/(1+sinα)+sinα根号下(1-cosα)/(1+cosα)

α为第四象限角
cosα*根号{(1-sinα)/(1+sinα)}+sinα根号{(1-cosα)/(1+cosα)}
= cosα*根号{(1-sinα)^2/(1-sin^2α)}+sinα根号{(1-cosα)^2/(1-cos^2α)}
= cosα*根号{(1-sinα)^2/cos^2α)}+sinα根号{(1-cosα)^2/sin^2α)}
= cosα *(1-sinα)/cosα + sinα *(1-cosα)^2/(-sinα)
= (1-sinα) -(1-cosα)
=cosα-sinα