问题描述: 证明sec x+tanx=tan(π/4 +x/2) 1个回答 分类:综合 2014-11-24 问题解答: 我来补答 sec x+tanx=1/cosx+sinx/cosx=(1+sinx)/cosxtan(π/4 +x/2)=[tanπ/4+tan(x/2)]/[1-tan(x/2)]=[1+tan(x/2)]/[1-tan(x/2)]=[(cos(x/2)+sin(x/2)]/[(cos(x/2)-sin(x/2)]=[(cos(x/2)+sin(x/2)]²/[(cos(x/2)-sin(x/2)][(cos(x/2)+sin(x/2)]=[cos²(x/2)+sin²(x/2)+2cos(x/2)sin(x/2)]/[cos²(x/2)-sin²(x/2)]=(1+sinx)/cosx所以,sec x+tanx=tan(π/4 +x/2) 展开全文阅读