若α角的终边过点P(-1,-2),则(sinα+cosα/sinα-cosα)+cos^2α=?
问题描述：
若α角的终边过点P(-1,-2),则(sinα+cosα/sinα-cosα)+cos^2α=?
答
tanα=2
cosα=-√5/5
(sinα+cosα)/(sinα-cosα)+cos^2α
=(sinα/cosα+cosα/cosα)/(sinα/cosα-cosα/cosα)+cos^2α
=(sinα/cosα+1)/(sinα/cosα-1)+cos^2α
=(tanα+1)/(tanα-1)+(-√5/5)^2
=(2+1)/(2-1)+1/5
=3+1/5
=16/5