若角α的终边落在直线x+2y=0上,则sinα+cosα/sinαcosα的值等于
问题描述:
若角α的终边落在直线x+2y=0上,则sinα+cosα/sinαcosα的值等于
答
若角α的终边落在直线x+2y=0
tanα=-1/2 (90<α<180)
1+tan²α=1/cos²α
cosα=-2√5/5
(sinα+cosα)/sinαcosα
=1/cosα+1/sinα
=sinα+cosα
=cosα(tanα+1)
=-2√5/5 ×1/2
=-√5/5