tan(a+π／4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(tana+1)/(1-tana)
=2
即1+tana=2(1-tana)
解得：tana=1/3
则sina=±√10/10
cos2a=1-2sin²a=1-2*(±√10/10)²=4/5