若4sin²α-5sinαcosα-cos²α=2,则tanα=

问题描述:

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+22tan²α-5tanα-3=0(2tanα+1)(tanα-3)=0tanα=-1/2或tanα=3