已知sin^2a+sin2acosa-cos2a=1,a∈(0,π/2),求sina,tana的值(详细过程)

sin^2a+sin2acosa-cos2a=1=sin^a +cos^a
sin^2a+sin2acosa=cos^a-sin^a+sin^a +cos^a
=2cos^a
4sin^acos^a+2sinacos^a=2cos^a
2sin^a+sina=1
(2sina-1)(sina+1)=0
sina=1/2 或 sina=-1（舍去）（a∈(0,π/2),）
a=30°
tana=3的1/3次方!