等式2边同时平方得：
(sinα)^2-4sinαcosα+4(cosα)^2=5/2
1-2sin2α+3(cosα)^2=1+3/2
3(cosα)^2-2sin2α=3/2
∵cos2α=2(cosα)^2-1
∴1.5cos2α=3(cosα)^2-1.5,此式2边同时乘以1.5得：
3(cosα)^2=1.5+1.5cos2α
1.5=3/2
则有
1.5+1.5cos2α-2sin2α=3/2
1.5cos2α=2sin2α
3cos2α=4sin2α
tan2α=3/4