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

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

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