Question

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

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