连AC交BD于O,
∵正方体AC1,
∴CC1⊥底面BD,AC⊥BD,
∴C1O⊥BD,
∴∠COC1是二面角C-BD-C1的平面角.
CO=AC/2=a√2/2,CC1=a,
∴tanCOC1=CC1/CO=√2,为所求.