∴ t = 2π π = 2, and the maximum value is 1.

Let P be the PD⊥x axis in D, then AD is a quarter period, AD= 12, DB=32, DP= 1

There are tan∠APD= 12 and tan∠BPD=32 in right triangle.

So tan ∠ APB = Tan (∠ APD+∠ BPD) =12+321? 12×32=8.

So choose B.