sinα-2cosα=√10/2 sin²α+4cos²α-4sinαcosα=10/4=5/2 1+3cos²α-4sinαcosα=5/2
3cos²α-4sinαcosα=3/2
(3-4tanα)/(tan²α+1)=3/2
整理得
3tan²α+8tanα-3=0
tanα=1/3或tanα=-3
tan2α=2tanα/(1-tan²α)=3/4