∵y=sinxcosx+

3

cos2x-

3

=

1

2

sin2x+

3

•

1+cos2x

2

-

3

=

1

2

sin2x+

3

2

cos2x-

3

2

=sin（2x+

π

3

）-

3

2

令2x+

π

3

=kπ+

π

2

可得x=

1

2

kπ+

π

12

令k=0可得满足条件的对称轴为x=

π

12

故选C