Question

设tanα/tanα-1=-1,则sin2α+sinαcosα+cos2α分之7等于

急啊！马上要，要过程

Answer 1

由题知，
设tanα/(tanα-1)=-1
所以，
tanα=1/2
tan2α
=(2tanα)/(1-tan²α)
=1/(3/4)
=4/3

所以，sin2α=4/5,cos2α=3/5
或sin2α=-4/5,cos2α=-3/5

所以，
7/(sin2α+sinαcosα+cos2α)
=7/(1.5*sin2α+cos2α)
=±35/9

Answer 2

tana = 1-tana
tana = 1/2 sina =1/根号5 cosa = 2/根号5

原式= 7/(2sinacosa +sinacosa +2cosa^2 -1)
= 7/(3* 2/5 +2 * 4/5 -1)
=35/ 9