若4sin²α-5sinαcosα-cos²α=2,则tanα=

若4sin²α-5sinαcosα-cos²α=2,则tanα=
若4sin²α-5sinαcosα-cos²α=2,则tanα=

若4sin²α-5sinαcosα-cos²α=2,则tanα=
4sin²α-5sinαcosα-cos²α=2=2(sin²α+cos²α)
两边同除以cos²α,得
4tan²α-5tanα-1=2tan²α+2
2tan²α-5tanα-3=0
(2tanα+1)(tanα-3)=0
tanα=-1/2或tanα=3